The equation of the perpendicular line to line CD and passes through point E is y = [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
The relation between the slopes of the perpendicular lines is
The form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
∵ The equation of line CD is y - 5 = -3(x + 2)
- Let us put it in the form of y = m x + b to find its slope m
∴ y - 5 = -3(x) + -3(2)
∴ y - 5 = -3x + -6
∴ y - 5 = -3x - 6
- Add 5 to both sides
∴ y = -3x - 1
- The slope of the line in this form is the coefficient of x
∴ m = -3
∴ The slope of the given line CD is -3
To find the slope of the perpendicular line on line CD reciprocal the slope of the line CD and change its sign
∵ The reciprocal of -3 is [tex]-\frac{1}{3}[/tex]
- Change its sign
∴ The slope of the perpendicular line to line CD is [tex]\frac{1}{3}[/tex]
- Substitute it in the form of the equation
∴ y = [tex]\frac{1}{3}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The perpendicular line to line CD passes through point E
∵ The coordinates of point E is (6 , -1)
∴ x = 6 and y = -1
∵ -1 = [tex]\frac{1}{3}[/tex] (6) + b
∴ -1 = 2 + b
- Subtract 2 from both sides
∴ -3 = b
- Substitute it in the equation
∴ y = [tex]\frac{1}{3}[/tex] x + (-3)
∴ y = [tex]\frac{1}{3}[/tex] x - 3
The equation of the perpendicular line to line CD and passes through point E is y = [tex]\frac{1}{3}[/tex] x - 3
Learn more:
You can learn more about the perpendicular line in brainly.com/question/2601054
#LearnwithBrainly
