Q19 - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1. Write down the given information.

The given circle Q has 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.

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

.

Step 4. Conclusion.

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