The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1
Step-by-step explanation:
Let us revise some rules
∵ A line has endpoints (-7 , -2) and (5 , 4)
∴ [tex]x_{1}[/tex] = -7 and [tex]x_{2}[/tex] = 5
∴ [tex]y_{1}[/tex] = -2 and [tex]y_{2}[/tex] = 4
- Use the formula of the slope up to find the slope of the line
∴ [tex]m=\frac{4-(-2)}{5-(-7)}=\frac{4+2}{5+7}=\frac{6}{12}=\frac{1}{2}[/tex]
To find the slope of the perpendicular line to the given line reciprocal it and change its sign
∵ The slope of the given line = [tex]\frac{1}{2}[/tex]
∴ The slope of the perpendicular line = -2
∵ The perpendicular line is a bisector of the given line
- That means the perpendicular line intersect the given line
at its midpoint
∵ The mid point of the given line = [tex](\frac{-7+5}{2},\frac{-2+4}{2})[/tex]
∴ The mid point of the given line = [tex](\frac{-2}{2},\frac{2}{2})[/tex]
∴ The mid point of the given line = (-1 , 1)
Now we wand to find the equation of the line whose slope is -2 and passes through point (-1 , 1)
∵ The form of the equation is y = mx + b, where m is the slope
and b is the y-intercept
∵ m = -2
- Substitute the value of m in the form of the equation
∴ y = -2x + b
- To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ Point (-1 , 1) lies on the line
∴ x = -1 and y = 1
∵ 1 = -2(-1) + b
∴ 1 = 2 + b
- Subtract 2 from both sides
∴ -1 = b
- Substitute the value of b in the equation
∴ y = -2x + (-1)
∴ y = -2x - 1
The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1
Learn more:
You can learn more about the equations of the perpendicular lines in brainly.com/question/9527422
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