Question

If A(–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a and b

Answer 1

We know that the diagonals of a parallelogram bisect each other.

Therefore, the coordinates of the mid-point of AC are same as the coordinates of the mid-point of BD i.e.,

`( \frac{-2+4}{2},\ \frac{-1+b}{2})=( \frac{a+1}{2},\frac{0+2}{2})`

`\Rightarrow ( 1,\ \frac{b-1}{2})=( \frac{a+1}{2},\ 1) `

`\Rightarrow \frac{a+1}{2}=1\text{ and }\frac{b-1}{2}=1`

⇒ a + 1 = 2 and b – 1 = 2

⇒ a = 1 and b = 3