Question

Circle Q has diameter $\overline{AB}$. If Ais at point localid="1648631574175" $\left(-3,5\right)$and center is at$\left(2,3\right)$ . Find the coordinates of point B.

Short answer

The coordinates of point B is$\left(7,1\right)$.

Step-by-step solution

Step 1. Write down the given information.

The given circle Qhas diameter AB, whose center is say $O\left(2,3\right)$and one end point is$A\left(-3,5\right)$.

Step 2. Concept used.

If a line segment has end-points at$\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$then the midpoint of the segment has coordinates $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 3. Calculation.

The coordinates of point B say $\left(h,k\right)$can be evaluated by using the midpoint formula.

$\begin{array}{c}\text{Midpointof}AB=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \left(2,3\right)=\left(\frac{-3+h}{2},\frac{5+k}{2}\right)\\ 2=\frac{-3+h}{2},3=\frac{5+k}{2}\\ h-3=4,k+5=6\\ h=7,k=1\end{array}$

.

Step 4. Conclusion.

The coordinates of point B is $\left(7,1\right)$.