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)

Step-by-step explanation

Step 1

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

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

Step 3

solve for x and y

`\begin{gathered} 7=(9+x_u)/(2) \\ 14=9+x_u \\ x_u=14-9 \\ x_u=5 \end{gathered}`

and

`\begin{gathered} 5=(8+y_u)/(2) \\ 10=8+y_u \\ 10-8=y_u \\ y_u=2 \end{gathered}`

I hope this helps you