# FIND EQUATION OF THE LINE PERPENDICULAR TO GIVEN LINE

If the two lines are perpendicular, then the product of their slopes is equal to - 1

m1 x m2  =  -1

By choosing any one of the points on the line and the slope, we can get the equation using the formula given below.

(y - y1) = m(x - x1)

Write down the equation of the line perpendicular to the line 1 and passing through A.

Problem 1 :

Solution :

Choosing two points from the line (0, -2) and (2, 0).

Slope (m) = (0 + 2)/(2 - 0)

m = 2/2

m = 1

Slope of the perpendicular line, which passes through the point A is -1.

Equation of the line passes through A (0, 4) is :

y - 4 = -1(x - 0)

y - 4 = -x

y = -x + 4

So, equation of the required line is y = -x + 4.

Problem 2 :

Solution :

Choosing two points from the line (1, 0) and (0, 4).

Slope (m) = (4 - 0)/(0 - 1)

m = 4/(-1)

m = -4

Slope of the perpendicular line, which passes through the point A is 1/4.

Equation of the line passes through A (0, 0) is :

y - 0 = (1/4)(x - 0)

y = x/4

So, equation of the required line is y = x/4.

Problem 3 :

Solution :

Choosing two points from the line (0, -8) and (1, 2).

Slope (m) = (2 - (-8))/(1 - 0)

m = (2+8)/1

m = 10

Slope of the perpendicular line, which passes through the point A is -1/10.

Equation of the line passes through A (0, 9) is :

y - 9 = (-1/10)(x - 0)

10(y - 9) = -x

10y - 90 =-x

y = (-1/10)x + (90/10)

y = (-1/10)x + 9

So, equation of the required line is y = (-1/10)x + 9.

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