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The equation of the perpendicular bisector is y = x + 2
Step-by-step explanation:
Let us revise the relation between the slopes of perpendicular lines
- The product of the slopes of two perpendicular lines is -1
- That means if the slope of one of them is m, then the slope of the other is
- You reciprocal the slope of one and change its sign to find the slope of the other
The mid point of a segment whose endpoints are and
is
The perpendicular bisector of a line is the line that intersect it in its mid-point and formed 4 right angles
∵ The end point of a given line are (9 , -3) and (-5 , -7)
∴ and
∴ and
- Find the slope of the line by using the rule of the slope
∵
∴ The slope of the given line is
To find the slope of the perpendicular bisector of it reciprocal it and change its sign
∴ The slope of the perpendicular bisector =
∵ The form of the linear equation is y = mx + b, where m is the
slope and b is the y-intercept
- Substitute the value of m in the equation
∴ The equation of the perpendicular bisector is y = x + b
To find b substitute x and y in the equation by a point on the line
∵ The perpendicular bisector of the given line intersect it at
its midpoint
- Find the mid-point of the given line busing the rule above
∵ and
∵ and
∴ The mid-point of the given line =
Point (2 , -5) is also lies on the perpendicular line
∴ x = 2 and y = -5
- Substitute them in the equation
∵ -5 = (2) + b
∴ -5 = -7 + b
- Add 7 to both sides
∴ 2 = b
- Substitute the value of b in the equation
∴ The equation of the perpendicular bisector is y = x + 2
The equation of the perpendicular bisector is y = x + 2
Learn more:
You can learn more about the linear equation in brainly.com/question/11223427
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