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 lengt

Answer 1

Length of a line given two points is given by:

`l= √((x_2-x_1)^2+(y_2-y_1)^2) \\ AB= √((-5-1)^2+(-2-6)^2) \\ = √((-6)^2+(-8)^2) \\ = √(36+64) \\ = √(100) \\ =10 \\ \\ CD= √((3-(-5))^2+(5-(-1))^2) \\ = √((3+5)^2+(5+1)^2) \\ = √(8^2+6^2) \\ = √(64+36) \\ = √(100) \\ =10`
Since |AB| = |CD|, points A, B, C, D form a parallelogram.