Question

Only answer number 37.

Answer 1

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.