Question

knowing the points a(1, 6), b(−5, −2), c(−1, −5), and d(5, 3), and that segment ab is parallel to segment cd, what is the length of segment ab and segment cd comma and do points a, b, c, and d form a parallelogram? hint: to prove these points form a parallelogram, segment ab and segment cd must be equal in length

Answer 1

Length of a line given two points is given by:
 $l= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AB= \sqrt{(-5-1)^2+(-2-6)^2} \\ = \sqrt{(-6)^2+(-8)^2} \\ = \sqrt{36+64} \\ = \sqrt{100} \\ =10 \\ \\ CD= \sqrt{(3-(-5))^2+(5-(-1))^2} \\ = \sqrt{(3+5)^2+(5+1)^2} \\ = \sqrt{8^2+6^2} \\ = \sqrt{64+36} \\ = \sqrt{100} \\ =10$
Since |AB| = |CD|, points A, B, C, D form a parallelogram.