9-4 Polygons in the Coordinate Plane

Learn to draw polygons in the coordinate plane and find the lengths of their sides.

9-4 Polygons in the Coordinate Plane

Remember that in a rectangle, opposite sides have equal length.

Helpful Hint

9-4 Polygons in the Coordinate Plane Additional Example 1: Drawing Polygons in the Coordinate

PlaneGraph the triangle with vertices F(2, 5), G(4, 1), and H(0, 22).

Graph each point on the coordinate plane.

Then connect the points with straight lines to form a polygon.

9-4 Polygons in the Coordinate Plane

Check It Out: Example 1

Graph the triangle with vertices A(1, 2), B(4, 2), and C(3, 1).

Graph each point on the coordinate plane.

Then connect the points with straight lines to form a polygon.

9-4 Polygons in the Coordinate Plane Additional Example 2: Finding Distance in the Coordinate

Plane

Find the perimeter of the rectangle.

Step 1: Find the length and width.To find the length of the rectangle, count from left to right along the x-axis from –1 to 3. The length is 4 units long. To find the width, count up the y-axis from –2 to 4. The width is 6 units long.

9-4 Polygons in the Coordinate Plane

Additional Example 2: Continued

Step 2: Find the perimeter. Use the formula for the perimeter of a rectangle.

Length of the rectangle = l

Width of the rectangle = w

Perimeter = 2l + 2w

P = 2(4) + 2(6) = 20

The perimeter of the rectangle is 20 units.

9-4 Polygons in the Coordinate Plane

Check It Out: Example 2

Find the perimeter of the rectangle.

Step 1: Find the length and width.To find the length of the rectangle, count from left to right along the x-axis from 5 to 8. The length is 3 units long. To find the width, count up the y-axis from 0 to 10. The width is 10 units long.

9-4 Polygons in the Coordinate Plane

Continued: Check It Out: Example 2

Step 2: Find the perimeter. Use the formula for the perimeter of a rectangle.

Length of the rectangle = l

Width of the rectangle = w

Perimeter = 2l + 2w

P = 2(3) + 2(10) = 26

The perimeter of the rectangle is 26 units.

9-4 Polygons in the Coordinate Plane

Candice’s house is at the corner of 3rd Avenue and 7th Street. She walks from her house west to Minus 2nd Avenue, then south to 4th Street, then east to 3rd Avenue, and then back home. How far did she walk?

Additional Example 3: Social Studies Application

Step 1: Plot the points and draw the rectangle.Step 2: Find the length and width of the rectangle.Step 3: Find the perimeter.

Perimeter = 2l + 2w P = 2(5) + 2(3) = 16

Candice walked 16 blocks.

9-4 Polygons in the Coordinate Plane

A polygon has vertices at (2, 4), (3, 4), (3, 1), and (2, 1). What type of polygon is this? What is its perimeter?

Check It Out: Example 3

The polygon is a rectangle. The perimeter is 8 units