Respuesta :
The Solution:
Step 1: The given data
The coordinates of the midpoint of MN is (4,1)
The coordinates of point of M is (-2,5)
The coordinates of point of N is (x,y)
Step 2:
The formula for calculating Midpoint coordinates is given below:
[tex]\text{Midpoint of MN=(}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(4,1)[/tex]In this case,
[tex]\begin{gathered} x_1=-2,y_1=5 \\ x_2=x,y_2=y \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} 4\text{=}\frac{-2_{}+x_{}}{2} \\ \text{cross multiplying, we get} \\ -2+x=4\times2 \end{gathered}[/tex][tex]\begin{gathered} -2+x=8 \\ x=8+2=10 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 1\text{=}\frac{5_{}+y_{}}{2} \\ \text{cross multiplying, we get} \\ 5+y=2\times1 \end{gathered}[/tex][tex]y=2-5=-3[/tex]Hence, the coordinates of point N is (10,-3)
