Question

First part of 15th question....
Please answer as soon as possible.

Answer 1

Answer:

a = 1,  b = 1

Step-by-step explanation:

Given A = (-2, 1), B = (a, 0), C = (4, b), D = (1, 2).

ABCD is parallelogram when B - A = C - D, or in other words, when:

- the difference between the x-coordinates from A to B is equal to the difference between the x-coordinates from D to C, so the horizontal shift in each case is the same;

- the difference between the y-coordinates from A to B is equal to the difference between the y-coordinates from D to C, so the vertical shift in each case is the same;

- so combined, the shift from A to B is the same as the shift from D to C, meaning that AB and DC are equal and parallel.

So looking at x-coordinates, we need

a - (-2) = 4 - 1  =>  a = 3 - 2 = 1

and looking at y-coordinates, we need

0 - 1 = b - 2  =>  b = 2 - 1 = 1.