Chapter 8: Q19 (page 415)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Write down the given information.

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

Step 2. Concept used.

If a line segment has end-points at $(x_{1}, y_{1}) and (x_{2}, y_{2})$ then the midpoint of the segment has coordinates $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

Step 3. Calculation.

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

\begin{matrix} Midpointof A B = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ (2, 3) = (\frac{- 3 + h}{2}, \frac{5 + k}{2}) \\ 2 = \frac{- 3 + h}{2}, 3 = \frac{5 + k}{2} \\ h - 3 = 4, k + 5 = 6 \\ h = 7, k = 1 \end{matrix}

Step 4. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Circle Q has diameter AB¯. If Ais at point localid="1648631574175" -3,5and center is at2,3 . Find the coordinates of point B.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Logic and Functions

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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