Question

Write the equation of a line over which A(-3,5) reflects to A’(2,-5). BRAINLIEST TO THE 1ST PERSON!!

Answer 1

Given two points:
A = (x₁,y₁) = (-3,5)
A' = (x₂,y₂) = (2,-5)

Find the midpoint of point A and point A'
The midpoint of the two points lies on the reflection line. You can find the midpoint by this following formula
x midpoint = $\dfrac{x_{1}+x_{2}}{2}$
y midpoint = $\dfrac{y_{1}+y_{2}}{2}$

Plug in the numbers
x midpoint = $\dfrac{-3+2}{2}$
x midpoint = $\dfrac{-1}{2}$
x midpoint = -0.5

y midpoint = $\dfrac{5+(-5)}{2}$
y midpoint = $\dfrac{0}{2}$
y midpoint = 0

The midpoint is
(x,y) = (-0.5, 0)

Find the slope of the line passes through (-3,5) and (2,-5)
Use this following formula to find the slope
m = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Plug in the numbers
m = $\dfrac{-5-5}{2-(-3)}$
m = $\dfrac{-10}{2+3}$
m = -10/5
m = -2

Find the slope of the line which is perpendicular to the line that passes through (-3,5) and (2,-5)
The line whose slope we want to find is the reflection line we are looking for. Two perpendicular lines have the rule of slope as follows.
m₁ × m₂ = -1

Input the numbers
-2 × m₂ = -1
m₂ = $\dfrac{-1}{-2}$
m₂ = $\dfrac{1}{2}$

Find the line equation
The reflection line has the slope of 1/2 and passes through the midpoint (-0.5, 0)
The formula to find a line equation:
y - y₁ = m(x - x₁)

Input the numbers (m = 1/2, x₁ = -0.5, y = 0)
y - y₁ = m(x - x₁)
y - 0 = 1/2 (x - (-0.5))
y = 1/2 (x + 0.5)
y = $\frac{1}{2}x+0.25$
This is the line equation

Answer 2

Not sure but (-2,5) and (1,3)