Chapter 13, Problem 15RP

To determine

To find: The value of the point $C$ .

Answer to Problem 15RP

Thecoordinate for the point is C is $\left(2,3\right)$ .

Explanation of Solution

Given:

The given point is $A\left(-6,1\right)$ and $B\left(2,3\right)$ .

Calculation:

The formula for the midpoint is,

  $M=\left(\frac{\left(x_1+x_2\right)}{2},\frac{\left(y_1+y_2\right)}{2}\right)$

Then for the midpoint B the point for C is obtained as,

  $\begin{array}{l}B=\left(\frac{\left(x+\left(-6\right)\right)}{2},\frac{\left(y+1\right)}{2}\right)\\ \left(2,3\right)=\left(\frac{\left(x+\left(-6\right)\right)}{2},\frac{\left(y+1\right)}{2}\right)\end{array}$

Then for $x$ ,

  $\begin{array}{l}\frac{\left(x+\left(-6\right)\right)}{2}=2\\ x=10\end{array}$

Then for $y$ ,

  $\begin{array}{l}\frac{\left(y+1\right)}{2}=3\\ y=5\end{array}$

Thus, the coordinate for the point is C is $\left(2,3\right)$ .