Answer:
The other endpoint of the segment is [tex](-18,-7)[/tex].
Step-by-step explanation:
The midpoint of the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the following formula:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
where [tex](x_m,y_m)[/tex] = coordinates of the midpoint.
We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:
[tex](-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2} )[/tex]
To find [tex]x_1[/tex] we need to solve this equation:
[tex]-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18[/tex]
and to find [tex]y_1[/tex] we need to solve this equation:
[tex]2= \frac{y_1+11}{2} \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7[/tex]
The other endpoint of the segment is [tex](x_1,y_1)=(-18,-7)[/tex].
