If the two lines are perpendicular, then the product of their slopes is equal to - 1
m_{1} x m_{2} = -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 - y_{1}) = m(x - x_{1})
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM