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.
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Find the equations of the diagonals of a rectangle whose sides are x = – 1, x = 2, y = – 2 and y = 6.
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Given,
The equations of sides of a rectangle are
x1 = -1, x2 = 2, y1 = -2, y2 = 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
= y2 – y1/ x2 – x1
= (6 + 2)/ (2 + 1)
= 8/3 = m
So, the equation of AC will be
y – y1 = m (x – x1)
y + 2 = 8/3 (x + 1)
3y + 6 = 8x + 8
⇒ 8x – 3y + 2 = 0