Question

The coordinates of the midpoint of MN are (4,1). The coordinates of point M are (-2,5).What are the coordinates of point N?

Answer 1

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:

$\text{Midpoint of MN=(}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(4,1)$

In this case,

$\begin{gathered} x_1=-2,y_1=5 \\ x_2=x,y_2=y \end{gathered}$

Substituting these values in the formula above, we get

$\begin{gathered} 4\text{=}\frac{-2_{}+x_{}}{2} \\ \text{cross multiplying, we get} \\ -2+x=4\times2 \end{gathered}$$\begin{gathered} -2+x=8 \\ x=8+2=10 \end{gathered}$

Similarly,

$\begin{gathered} 1\text{=}\frac{5_{}+y_{}}{2} \\ \text{cross multiplying, we get} \\ 5+y=2\times1 \end{gathered}$$y=2-5=-3$

Hence, the coordinates of point N is (10,-3)