Question

For questions 2 and 3 plot the points in the coordinate plane. Then determine whether AB and CD are congruent. Explain your answer.
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Answer 1

Answer:

  2. congruent

  3. congruent

Step-by-step explanation:

Segments will be congruent if their lengths are the same. Their lengths will be the same if the sum of squares of the x- and y-differences of their endpoint coordinates are the same.

2. B-A = (-4-(-4), 8-1) = (0, 7)

  D-C = (5-(-2), -5-(-5)) = (7, 0)

The total of 0² and 7² is the same as the total of 7² and 0², so these segments are congruent. (They are both of length 7.)

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3. B-A = (2-4, 6-1) = (-2, 5)

  D-C = (-4-(-2), -3-2) = (-2, -5)

The sum of (-2)² and 5² is the same as the sum of (-2)² and (-5)², so these segments are congruent. (They both are of length √29.)