Only answer number 37.

Question

asked Sep 22, 2022 171k views

1 Answer

Blgt · Answer 1 · 2022-09-26T09:35:39+0000

Explanation:

Use the distance formula:

(x2, y2) with (x1, y1)

$d \: = \sqrt{( x2 \: - \: x1) {}^(2) \: + \: (y2 \: - \: y1) {}^(2) }$

Find the lengths of each segment one at a time.

For AC:

A(-3,8) C(0,2)

$d = \sqrt{( - 3 - 0) {}^(2) + (8 - 2) {}^(2) }$

$d \: = √(9 + 36)$

$d \: = √(45) = 3 √(5)$

For BC:

B(6,5) C(0,2)

$d \: = \sqrt{(6 - 0) ^(2) + (5 - 2) {}^(2) }$

$d \: = √(36 + 9)$

$d \: = √(45) = 3 √(5)$

For CD:

C(0,2) D(2,-4)

$d \: = \sqrt{(0 - 2) {}^(2) + (2 - ( - 4)) {}^(2) }$

$d \: = √(4 + 36)$

$d \: = √(40) = 2 √(10)$

With all the segment lengths found, we can conclude that segments AC and BC have the same lengths.