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. [3 MARKS]

Answer 1

Formula: 1 Mark
Application: 1 Mark
Answers: 1 Mark

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

$\therefore$ The coordinates of the mid-point of AC = The coordinates of the mid-point of BD i.e.

If $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$ and $D(x_4,y_4)$ are the vertices of parallelogram ABCD, Then

$\frac{x_1+x_3}{2},\frac{y_1+y_3}{2}=\frac{x_2+x_4}{2},\frac{y_2+y_4}{2}$

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

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

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

$\Rightarrow a+1=2andb-1=2$

$\Rightarrow a=1andb=3$