Find the best answers to your questions with the help of IDNLearn.com's expert contributors. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
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)