Question

If the points A(1, 1), B(2, 10), C(4, b) and D(a, - 8) are the vertices of a parallelogram ABCD, find the values of a and b.​

Answer 1

To find the values of a and b for the parallelogram ABCD, we can use the properties of parallelograms. The value of a is found to be 5, but there is no valid value for b.

Step-by-step explanation:

To determine the values of a and b for a parallelogram ABCD with vertices A(1, 1), B(2, 10), C(4, b), and D(a, -8), we can use the properties of parallelograms.

In a parallelogram, opposite sides are equal in length and parallel.

Using this information, we can set up equations based on the coordinates of the vertices:

AB = CD: (2-1) = (a-4) => 1 = a-4 => a = 5

BC = AD: (10-1) = (-8-(-8)) => 9 = 0 => There is no value of b that satisfies this equation.

Therefore, the value of a is 5, but there is no valid value for b.