Question

If A = (-2, -1), B = (a, 0), C = (4, b) and D ( 1, 2) are the vertices of a parallelogram ABCD. Find the values of a and b. Also find midpoint of AC.

Answer 1

Answer:

The side AB = CD

${( - 2 - a)}^{2} + 1 = {(4 - 1)}^{2} + \\ {(b - 2)}^{2} \\ \\ 4 + {a}^{2} + 4a = \\ 9 + {b}^{2} + 4 - 4b \\ \\ {a}^{2} + 4a = {b}^{2} - 4b$

And

AD = BC

${3}^{2} + {3}^{2} = {(a - 4)}^{2} + {b}^{2} \\ 18 = {a}^{2} + 16 - 8a + {b}^{2} \\ {a}^{2} - 8a + {b}^{2} = 2$