An Important Question of M.L Aggarwal book of class 10 Based on Equation of a Straight Line Chapter for ICSE BOARD.
Here Given that:
(i) A line meets the x-axis at A. Write down the co-ordinates of A.
(ii) Determine the equation of the line passing through A and perpendicular to 4x – 3y + 12 = 0.
This is the Question Number 18, Exercise 12.2 of M.L Aggarwal.
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(i) The line 4x – 3y + 12 = 0 meets the x-axis at A. Write down the co-ordinates of A. (ii) Determine the equation of the line passing through A and perpendicular to 4x – 3y + 12 = 0.
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Given line: 4x – 3y + 12 = 0
(i) When this line meets the x-axis, its y co-ordinate becomes 0.
So, putting y = 0 in the given equation, we get
4x – 3(0) + 12 = 0
4x + 12 = 0
x = -12/4
x = -3
Hence, the line meets the x-axis at A (-3, 0).
(ii) Now, the slope of the line is given by
4x – 3y + 12 = 0
3y = 4x + 12
y = (4/3) x + 4
⇒ m1 = 4/3
Let’s assume the slope of the line perpendicular to the given line be m2
Then, m1 x m2 = -1
4/3 x m2 = -1
m2 = -3/4
Thus, the equation of the line perpendicular to the given line passing through A will be
y – 0 = -3/4 (x + 3)
4y = -3(x + 3)
3x + 4y + 9 = 0