Question

Complete the coordinate proof of the theorem.

https://static.k12.com/nextgen_media/assets/8080753-NG_GMT_SemA_04_UT_06.png

Given: A B C D is a rectangle.
Prove: The diagonals of A B C D are congruent.

Enter your answers in the boxes.

The coordinates of rectangle ABCD are A(0, 0) , B(a, 0) , C(_____, _____), and D(0, b) .

The length of AC¯¯¯¯¯ is equal to _______.
.

The length of BD¯¯¯¯¯ is equal to ______.
.

The diagonals of the rectangle have the same length.

Therefore, AC¯¯¯¯¯ is congruent to BD¯¯¯¯¯.

Answer 1

@563blackghost

Answer 2

old questinon but wil answer so this can be closed

notice how C has the same x-coordinate as B, and the same y-coordinate as D. look at the coordinates of B and D to determine the coordinates of C.

for the length of AC, apply the distance formula to points A and C

for the length of BD, apply the distance formula to points B and D (shortcut method: since the diagonals are equal, length of BD = the length of AC from the previous step)