Question

If (1, 2) (4, y) (x, 6) and (3, 5) are the vertical of a parallelogram taken in order. Find x &Y.​

Answer 1

Solution :-

Let :-

The vertices of the parallelogram be A (1 , 2), B (4 , y), C (x , 6) and D (3 , 5).

We know :-

In a parallelogram diagonals bisect each other.

That is :-

Midpoints of AC = Midpoint of BD

$\bf Midpoint \ formula = \left( \dfrac{x_1+x_2}{2} \ , \ \dfrac{y_1+y_2}{2} \right)$

$\bullet \sf \ Midpoint \ of \ AC = \left( \dfrac{1+x}{2} \ , \ \dfrac{2+6}{2}\right)\\\\ \bullet \ Midpoint \ of \ BD = \left( \dfrac{4+3}{2} \ , \ \dfrac{y+5}{2} \right)$

$\longrightarrow \sf \dfrac{1+x}{2} = \dfrac{4+3}{2} \\\\\longrightarrow \dfrac{1+x}{2} = \dfrac{7}{2} \\\\\longrightarrow 2(1+x) = 14\\\\\longrightarrow 2+2x=14 \\\\\longrightarrow 2x=12 \\\\\longrightarrow\bf x = 6$

$\longrightarrow \sf \dfrac{2+6}{2} = \dfrac{y+5}{2} \\\\\longrightarrow \dfrac{8}{2} = \dfrac{y+5}{2} \\\\\longrightarrow 4 = \dfrac{y+5}{2} \\\\\longrightarrow y+5= 8 \\\\\longrightarrow \bf y = 3$

Value of x = 6

Value of y = 3