Question

Please help me for this question

Answer 1

Answer:

Mid-point: $(0,-5)$

Equation: $y=\frac{7}{3}x-5$

Step-by-step 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: $\frac{{y__2}-{y__1}}{{x__2}-{x__1}}$ = $\frac{{-8}-{-2)}}{{7}-{(-7)}}$ = $\frac{-6}{14}$ = $\frac{-3}{7}$

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

$\frac{-3}{7}*m = -1$

$m=\frac{7}{3}$

By the point slope form:

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

Plug in the coordinates of the mid-point:

$({y}-{(-5)})=\frac{7}{3} ({x}-{0})$

Equation: $y=\frac{7}{3}x-5$