Answer:
D: (15,13)
Step-by-step explanation:
So we know that the midpoint of CD is (5,6).
We also know that Point C is (-5,-1), and we want to find Point D.
Remember that the Midpoint Formula is:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Let's let Point C (-5,-1) be (x₁, y₁) and let's let Point D be (x₂, y₂)
We already know that the midpoint is (5,6). So:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(5,6)[/tex]
So:
[tex]\frac{x_1+x_2}{2}=5\text{ and } \frac{y_1+y_2}{2}=6[/tex]
Let's solve them individually.
For the first one, let's substitute -5 for x₁. So:
[tex]\frac{-5+x_2}{2}=5[/tex]
Multiply both sides by 2:
[tex]-5+x_2=10[/tex]
Add 5 to both sides:
[tex]x_2=15[/tex]
So, the x-coordinate of Point D is 15.
Do the same for the y-coordinate. Substitute -1 for y₁. So:
[tex]\frac{-1+y_2}{2}=6[/tex]
Multiply both sides by 2:
[tex]-1+y_2=12[/tex]
Add 1 to both sides:
[tex]y_2=13[/tex]
So, the y-coordinate of Point D is 13.
Therefore, Point D is (15,13).
And we're done!
