Complete the coordinate proof of the theorem. given: a b c d is a parallelogram. prove: the diagonals of a b c d bisect each other. enter your answers in the boxes. the coordinates of parallelogram abcd are a(0, 0) , b(a, 0) , c( , ), and d(c, b) . the coordinates of the midpoint of ac¯¯¯¯¯ are ( , b2 ). the coordinates of the midpoint of bd¯¯¯¯¯ are ( a+c2 , ). the midpoints of the diagonals have the same coordinates. therefore, ac¯¯¯¯¯ and bd¯¯¯¯¯ bisect each other.

The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C(a+c, b), and D(c, b)

The coordinates of the midpoint of AC are ((a+c)/2, b/2)

The coordinates of the midpoint of BD are ((a+c)/2, b/2)

Step-by-step explanation:

The x-coordinate of C is the addition of x-coordinates of D and B

The y-coordinate of C is the same as y-coordinates of D

The x-coordinate of the midpoint of AC are half of the distance in x-coordinate between A and C, that is, (a+c)/2

The y-coordinate of the midpoint of DB are half of the distance in y-coordinate between D and B, that is, b/2

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm