Answer:
The coordinates of point L are:
(x₁, y₁) = (-22, 17)
Step-by-step explanation:
We know that the Midpoint Formula is given by:
[tex]\left(x,\:y\right)=\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
In our case:
M(-12, 6) is the midpoint. Thus,
(x, y) = (-12, 6)
N(-2, -5) is the second point, Thus,
(x₂, y₂) = (-2,-5)
We have to determine the coordinates of point L.
Let (x₁, y₁) be the coordinates of point L.
substituting (x, y) = (-12, 6), (x₂, y₂) = (-2,-5) in the Midpoint Formula
[tex]\left(-12,\:6\right)=\left(\frac{-2+x_1}{2},\:\:\frac{-5+y_1}{2}\right)[/tex]
Determining the x₁ coordinate of the point L
[tex]\frac{-2+x_1}{2}=-12[/tex]
[tex]-2+x_1=-24[/tex]
Add 2 to both sides
[tex]-2+x_1+2=-24+2[/tex]
Simplify
[tex]x_1=-22[/tex]
Determining the y₁ coordinate of the point L
[tex]\frac{-5+y_1}{2}=6[/tex]
[tex]-5+y_1=12[/tex]
Add 5 to both sides
[tex]-5+y_1+5=12+5[/tex]
Simplify
[tex]y_1=17\:\:\:[/tex]
Therefore, the coordinates of point L are:
(x₁, y₁) = (-22, 17)
