4.7 Triangles and Coordinate Proof

Ex. 1: Placing a Rectangle in a Coordinate Plane

Place a 2-unit by 6-unit rectangle in a coordinate plane – many possible answers here!

One possible answer:

One vertex is at the origin, and three of the vertices have at least one coordinate that is 0.

6

4

2

-2

-4

-5 5

Ex. 1: Placing a Rectangle in a Coordinate Plane

Another possible answer:

One side is centered at the origin, and the x-coordinates are opposites.

4

2

-2

-4

-6

-5 5 10

Note: Once a figure has been placed in a coordinate plane,

you can use the Distance Formula or the Midpoint Formula to measure distances or locate points

What is the distance formula?

What is the midpoint formula?

Ex. 2: Using the Distance Formula

A right triangle has legs of 5 units and 12 units. Place the triangle in a coordinate plane. Label the coordinates of the vertices and find the length of the hypotenuse.

6

4

2

-2

-4

-6

-8

-10

5 10 15 20

Ex. 3 Using the Midpoint Formula

In the diagram L is the midpoint of the line segment; find the coordinates of point L.

160

140

120

100

80

60

40

20

-20

-40

-60

-80

-100

-120

-140

-160

-180

-50 50 100 150 200 250 300 350 400 450

L

Ex. 4

A right triangle has legs of 7 and 9 units; find the length of the hypotenuse.