Graphs

Rectangular Coordinates

Use the distance formula.

Use the midpoint formula.

Graphing ordered pairs.

x axis: horizontal line y axis: vertical line Origin: point of intersection of the two axes Rectangular (Cartesian) Coordinate Plane:

plane formed by the x-axis and the y-axis Divided into four sections called quadrants.

1st is upper right, 2nd is upper left, 3rd is lower left, 4th is lower right

Ordered Pair: (x, y) First value is the x coordinate (abscissa): tells

right and left movement Second value is the y coordinate (ordinate):

tells up and down movement

Graph the following ordered pairs and state what quadrant they are in (-2, 5)

Left 2, up 5: 2nd quadrant (-7, -2.5)

Left 7, down 2.5 (approximate the .5): 3rd quadrant

(0,8)No motion right and left, up 8: not in a quadrant

(3, -6)Right 3, down 6: 4th quadrant

Distance Formula

(1, 3) and (5, 6)Find horizontal distance by subtracting x’s.

5 – 1 = 4Find vertical distance by subtracting y’s.

6 – 3 = 3Pythagorean Theorem

a2 + b2 = c2 42 + 32 = c2

16 + 9 = c2 25 = c2 5 = c

Distance Formula

D = sqrt ((x2 – x1)2 + (y2 – y1)2))

Remember: This is an application of the Pythagorean Theorem

Find the distance between (-4,5) and (3,2) Sqrt ((-4 – 3)2 + (5 – 2)2) = d Sqrt (49 + 9) = d Sqrt 58 = d

Determine if the triangle formed by the coordinates (-2, 1), (2, 3), and (3,1) is an isosceles triangle. Find the length of each side by using the

distance formula.Sqrt((-2 – 2)2 + (1 – 3)2)) = Sqrt 20Sqrt((2 – 3)2 + (3 – 1)2) = Sqrt 5Sqrt((3 - -2)2 + (1 – 1)2 = Sqrt 25 = 5Not isosceles since no two sides are equal.If you test pythagorean theorem you will find that it

is a right triangle. (sqrt 20)2 + (sqrt 5)2 = (5)2

Midpoint Formula

To find the midpoint of a line segment, average the x-coordinates and average the y-coordinates of the endpoints.

M(x, y) = ( (x1 + x2)/2 , (y1 + y2)/2))

(-5, 5) to (3, 1) = (-5 + 3)/2 , (5 + 1)/2 (-2/2, 6/2) => (-1, 3)

Verify that the following is a right triangle, then find the area. (4, -3), (0, -3), (4, 2) Sqrt ((4 - 0)2 + (-3 - -3)2) = sqrt 16 = 4 Sqrt ((0 – 4)2 + (2 - -3)2) = sqrt (41) Sqrt ((4 – 4)2 + (2 - -3)2) = sqrt (25) = 5 Right triangle if a2 + b2 = c2. When testing remember

that ‘a’ and ‘b’ are the legs of the triangle, the shorter sides.

Does (sqrt 25)2 + (sqrt 16)2 = (sqrt 41)2? Yes to it is a right triangle. Area = ½ l w so Area = .5 (5) (4) = 10

Assignment

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