Step-by-step explanation:
Use the distance formula:
(x2, y2) with (x1, y1)
[tex] d \: = \sqrt{( x2 \: - \: x1) {}^{2} \: + \: (y2 \: - \: y1) {}^{2} } [/tex]
Find the lengths of each segment one at a time.
For AC:
A(-3,8) C(0,2)
[tex]d = \sqrt{( - 3 - 0) {}^{2} + (8 - 2) {}^{2} } [/tex]
[tex]d \: = \sqrt{9 + 36} [/tex]
[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]
For BC:
B(6,5) C(0,2)
[tex]d \: = \sqrt{(6 - 0) ^{2} + (5 - 2) {}^{2} } [/tex]
[tex]d \: = \sqrt{36 + 9} [/tex]
[tex]d \: = \sqrt{45} = 3 \sqrt{5} [/tex]
For CD:
C(0,2) D(2,-4)
[tex]d \: = \sqrt{(0 - 2) {}^{2} + (2 - ( - 4)) {}^{2} } [/tex]
[tex]d \: = \sqrt{4 + 36} [/tex]
[tex]d \: = \sqrt{40} = 2 \sqrt{10} [/tex]
With all the segment lengths found, we can conclude that segments AC and BC have the same lengths.
