This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.

Here you have to find the equations of the diagonals of a rectangle whose sides are given in the question

This is the Question Number 31, Exercise 12.1 of M.L Aggarwal.

# Find the equations of the diagonals of a rectangle whose sides are x = – 1, x = 2, y = – 2 and y = 6.

Share

Given,

The equations of sides of a rectangle are

x

_{1}= -1, x_{2}= 2, y_{1}= -2, y_{2}= 6.These lines form a rectangle when they intersect at A, B, C, D respectively

Now,

The co-ordinates of A, B, C and D will be (-1, -2), (2, -2), (2, 6) and (-1, 6) respectively.

And, AC and BD are its diagonals

Slope of the diagonal AC

= y

_{2}– y_{1}/ x_{2}– x_{1}= (6 + 2)/ (2 + 1)

= 8/3 = m

So, the equation of AC will be

y – y

_{1}= m (x – x_{1})y + 2 = 8/3 (x + 1)

3y + 6 = 8x + 8

⇒ 8x – 3y + 2 = 0