Graph and label the point on the coordinate plane below. · To reflect across the x-axis, keep the...

Graph and label the point on the coordinate plane below.1. T(0, 0)

SOLUTION: The point (0, 0) is the origin, so point T should be graphed on the origin.

2. D(2, 1)

SOLUTION: From the origin, move 2 units to the right and 1 unit up.

3. K(–3.25, 3)

SOLUTION: Starting at the origin, move 3.25 units to the left and 3 units up.

SOLUTION:

From the origin, move units down.

5. F(–4.5, 0)

SOLUTION: From the origin, move 4.5 units to the left.

SOLUTION:

From the origin, move units to the left and then 3 units down.

7. L(2.5, –3.5)

SOLUTION: From the origin, move 2.5 units to the right and then 3.5 units down.

SOLUTION:

From the origin, move 4 units to the right and units up.

9. Graph U(3.5, –3) on the coordinate plane below. Then graph its reflection across the x-axis.

SOLUTION: Graph point U.

To reflect across the x-axis, keep the x-coordinate and take the opposite of the y-coordinate.

10. Graph B(–7, 6) on the coordinate plane below. Then graph its reflection across the x-axis.

SOLUTION: Graph point B.

To reflect across the x-axis, keep the same x-coordinate and take the opposite of the y-coordinate.

11. Graph R(–2, 5) on the coordinate plane below. Then graph its reflection across the y-axis.

SOLUTION: Graph point R.

To reflect across the y-axis, keep the same y-coordinate and take the opposite of the x-coordinate.

12. Amelia is drawing a map of the park. She graphs the entrance at (2, –3). She reflects (2, –3) across the y-axis. ThenAmelia reflects the new point across the x-axis. What figure is graphed on the map?

SOLUTION: Graph (2, –3) on the coordinate plane. (2, –3) reflected across the y-axis is (–2, –3). (–2, –3) reflected across the x-axis is (–2, 3).

The resulting figure is a triangle.

13. A point is reflected across the y-axis. The new point is located at (–4.25, –1.75). Write the ordered pair that represents the original point.

SOLUTION: When a point is reflected across the y-axis, the y-coordinate is kept the same and the opposite of the x-coordinate is used. If the resulting point is (–4.25, –1.75), the y-coordinate of the original point will be the same and the opposite ofthe x-coordinate is used. So, the original point is (4.25, –1.75).

14. Model with Mathematics A point is reflected across the x-axis. The new point is (–7.5, 6). What is the distance between the two points?

SOLUTION: When a point is reflected across the x-axis, the x-coordinate is kept the same, and the opposite of the y-coordinate is used. If the resulting point is (–7.5, 6), the original point is (–7.5, –6). To find the distance between the two points, subtract the y-coordinates since the x-coordinates are the same. 6 – (–6) = 12 So, the distance between the two points is 12 units.

15. On a coordinate plane, draw triangle ABC with vertices A(–1, –1), B(3, –1), and C(–1, 2). Find the area of the triangle in square units.

SOLUTION: First graph the points A, B, and C.

Next find the area of the triangle using A=b × h ÷ 2The base is 4 units and the height is 3. A = 4 × 3 ÷ 2 = 6 square units

16. The points (4, 3) and (–4, 0) are graphed on a coordinate plane. The point (4, 3) is reflected across the x- and y-axes. If all four points are connected, what figure is graphed?

SOLUTION: Graph the points (4, 3) and (–4, 0) on a coordinate plane.

Reflect the point (4, 3) across the x- and y-axes. Connect the points to form a figure.

The figure is a trapezoid.

17. Identify Structure Three vertices of a quadrilateral are (–1 –1), (1, 2), and (5, –1). What are the coordinates of twovertices that will form two different parallelograms?

SOLUTION: Graph the three vertices on a coordinate plane.

By using the three original points as the left sides and lower right, the fourth point at (7, 2) can be placed.

By using three original points as the right sides and lower left side, the fourth point at (–5, 2) can be placed.

Persevere with Problems Determine whether the statement is sometimes, always, or never true. Give an example or a counterexample.

18. When a point is reflected across the y-axis, the new point has a negative x-coordinate.

SOLUTION: sometimes; Sample answer: The x-coordinate of the new point will be negative if the x-coordinate of the original point is positive.

19. The point (x, y) is reflected across the x-axis. Then the new point is reflected across the y-axis. The location of the point after both reflections is (–x, –y).

SOLUTION: always; The y-coordinate will be the opposite of the original following the reflection across the x-axis. The x-coordinate will be the opposite of the original following the reflection across the y-axis.

20. The x-coordinate of a point lies on the x-axis is negative.

SOLUTION: sometimes; Sample answer: If the point is located to the left of the origin, the x-coordinate is negative (–2, 0), if the point is located to the right of the origin, the x-coordinate is positive (2, 0).

21. The x-coordinate of a point that lies on the y-axis is positive.

SOLUTION: never; The x-coordinate of any point on the y-axis is always zero.

Graph and label the point on the coordinate plane below.22. B(–3, 4)

SOLUTION: The x-coordinate is –3. The y-coordinate is 4.

23. D(–1.5, 2.5)

SOLUTION: The x-coordinate is –1.5. The y-coordinate is 2.5.

SOLUTION:

The x-coordinate is . The y-coordinate is .

SOLUTION:

26. C(1, 4.5)

SOLUTION: The x-coordinate is 1. The y-coordinate is 4.5.

27. F(–4, –3.5)

SOLUTION: The x-coordinate is –4. The y-coordinate is –3.5.

SOLUTION:

The x-coordinate is . The y-coordinate is 3.

SOLUTION:

The x-coordinate is –3. The y-coordinate is .

30. Graph N(1, –3) on the coordinate plane to the right. Then graph its reflection across the y-axis.

SOLUTION: Graph point N.

31. Graph H(7, 8) on the coordinate plane below. Then graph its reflection across the x-axis.

SOLUTION: Graph point H.

32. Graph F(–6, 5.5) on the coordinate plane to the right. Then graph its reflection across the x-axis.

SOLUTION: Graph point F.

33. Marcus is drawing a plan for his vegetable garden. He graphs one corner at (–7.5, 2) and one corner at (7.5, 2). He reflects (–7.5, 2) across the x-axis. Then Marcus reflects the new point across the y-axis. What shape is the vegetable garden?

SOLUTION: Graph (–7.5, 2) and (7.5, 2).

Reflect (–7.5, 2) across the x-axis.

Reflect the new point across the y-axis and connect the four points.

The resulting graph is a rectangle.

34. A point is reflected across the x-axis. The new point is located at (4.75, –2.25). Write the ordered pair that represents the original point.

SOLUTION: To reflect across the x-axis, keep the same x-coordinate and take the opposite of the y-coordinate. If the new point is located at (4.75, –2.25), then the original point has the same x-coordinate but the opposite y-coordinate. So the original point is at (4.75, 2.25).

35. Model with Mathematics A point is reflected across the x-axis. The new point is (5, –3.5). What is the distance between the two points?

SOLUTION: To reflect a point across the x-axis, keep the same x-coordinate and take the opposite of the y-coordinate. If the newpoint is (5, –3.5), then the original point is (5, 3.5). The distance between (5, –3.5) and (5, 3.5) can be found by subtracting the y-coordinates since the x-coordinates are the same. 3.5 – (–3.5) = 7 So, the distance between the two points is 7 units.

36. Draw triangle XYZ with vertices X(–3, 2), Y(4, –2), and Z(–3, –2) on the coordinate plane. Then find the area of the triangle in square units.

SOLUTION: First graph the coordinates.

Next find the area of the triangle using A = ½ ×b ×hThe base is 7 units and the height is 4 units. A= ½ × 7 × 4 = 14 square units

37. What are the coordinates of point H after it is reflected across the x-axis, and then reflected across the y-axis?

SOLUTION: To reflect the point (–2.5, 3.25) across the x-axis, keep the same x-coordinate and take the opposite of the y-coordinate. The new point is (–2.5, –3.25). To reflect this new point across the y-axis, keep the same y-coordinate and take the opposite of the x-coordinate. The new point is then (2.5, –3.25).

Multiply.38. 1 × 1 × 1

SOLUTION: Multiply the first two factors, then multiply the product by the third factor. So, 1 × 1 × 1 = 1.

39. 3 × 3 × 3

40. 6 × 6 × 6

SOLUTION: Multiply the first two factors, then multiply the product by the third factor. So, 6 × 6 × 6 = 216

41. Use the geometric pattern below to find the number of squares in the next figure.

SOLUTION: By counting the squares, the pattern is 1, 4, 9, 16 or 1², 2², 3², 4². So, the next number in the pattern is 5², or 25.

42. Alexa saved a total of $210. Each week she saved the same amount of money. She has been saving for 7 weeks. How much money did Alexa save each week?

SOLUTION: Since she saved the same amount each week, divide the total saved by the number of weeks. $210 ÷ 7 = $30. So, she saved $30 each week.

eSolutions Manual - Powered by Cognero Page 1

5-7 Graph on the Coordinate Plane

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

2. D(2, 1)

3. K(–3.25, 3)

SOLUTION:

5. F(–4.5, 0)

SOLUTION:

7. L(2.5, –3.5)

SOLUTION:

23. D(–1.5, 2.5)

SOLUTION:

26. C(1, 4.5)

27. F(–4, –3.5)

SOLUTION:

Multiply.38. 1 × 1 × 1

39. 3 × 3 × 3

40. 6 × 6 × 6

Graph and label the point on the coordinate plane below. · To reflect across the x-axis, keep the...

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Transcript of Graph and label the point on the coordinate plane below. · To reflect across the x-axis, keep the...