# 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 - Mathematics

Sum

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

#### Solution

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

Concept: Section Formula
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