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

Question

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

0

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 =
y midpoint =

Plug in the numbers
x midpoint =
x midpoint =
x midpoint = -0.5

y midpoint =
y midpoint =
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 =

Plug in the numbers
m =
m =
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 =
m₂ =

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 =
This is the line equation

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