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Please help me for this question

Please help me for this question-example-1
User NightEye
by
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1 Answer

12 votes

Answer:

Mid-point:
(0,-5)

Equation:
y=(7)/(3)x-5

Explanation:

To find the mid-point of AB, simply add up their x and y coordinates and divide by 2 respectively to find their middle point.


(\frac{{x__A}+{x__B}}{2},\frac{{y__A}+{y__B}}{2})


(\frac{{-7}+{7}}{2},\frac{{-2}+{(-8)}}{2})


(0,-5)

To find the perpendicular slope that passes through the mid-point, we need to know the slope between AB first.

Slope of AB:
\frac{{y__2}-{y__1}}{{x__2}-{x__1}} =
\frac{{-8}-{-2)}}{{7}-{(-7)}} =
(-6)/(14) =
(-3)/(7)

Multiplying slopes that are perpendicular with each other always results in -1.


(-3)/(7)*m = -1


m=(7)/(3)

By the point slope form:


({y}-{y__1})=m({x}-{x__1})

Plug in the coordinates of the mid-point:


({y}-{(-5)})=(7)/(3) ({x}-{0})

Equation:
y=(7)/(3)x-5

User Arinzehills
by
4.7k points