Question

TU has a midpoint at M(7,5). Point T is at (9,8). Find the coordinates of point U.

Answer 1

(5,2)

Explanation

Step 1

if you have 2 points P1 and P2 , the midpoint is given by:

$\text{Midpoint}=(\frac{x_1+x_{2,}}{2},\frac{y_1+y_2}{2})$

where

$\begin{gathered} P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}$

Let

T=(9,8)

Midpoint(7,5)

U=unknown

Step 2

replace

$\begin{gathered} \text{Midpoint}=(\frac{x_1+x_{2,}}{2},\frac{y_1+y_2}{2}) \\ (7,5)=(\frac{9+x_{u,}}{2},\frac{8+y_u}{2}) \\ \text{then} \\ 7=\frac{9+x_u}{2} \\ \text{and} \\ 5=\frac{8+y_u}{2} \end{gathered}$

Step 3

solve for x and y

$\begin{gathered} 7=\frac{9+x_u}{2} \\ 14=9+x_u \\ x_u=14-9 \\ x_u=5 \end{gathered}$

and

$\begin{gathered} 5=\frac{8+y_u}{2} \\ 10=8+y_u \\ 10-8=y_u \\ y_u=2 \end{gathered}$

I hope this helps you