Coordinate Proof Using Distance and Midpoint

(11, -7)

(-5.5, -3.5)

(5.5, -3.5)

(2, -2)

(5, -2)

(10, -6)

(5, -3)

(2, -2)

7.1

7.8

8.7

8.9

Find the midpoint of the diagonals.

Find the length of the diagonals.

Find the slope of the diagonals.

Diagonals in a rhombus are not perpendicular, so this is not a good method.

Find the lengths of the diagonals.

Find the slope of each diagonal.

Find the midpoint of each diagonal.

Find the midpoint of each side.

AB = CD

AB = CD and BC = AD

mCD ∙ mBC = -1

mAB = mCD

(5, -2)

(10, -6)

(5, -3)

(2, -2)

Slope

Midpoint

Distance

1

2

3

4

Yes, because AD = BC = 10 and AB = CD = 5

No because  $$AD=2\sqrt{10}$$  and  $$BC=10$$   

Yes because AD = BC = 5 and AB = CD = 10

No because  $$CD=\sqrt{73}$$  and  $$BC=5$$