Chapter 8: Q44. (page 416)

Point $D (5, - 1)$ is the midpoint of segment $\bar{C E}$ . If point Chas coordinates $(3, 2)$ then what are the coordinates of point E.
$(A) (8, 1) (B) (7, - 4) (C) (2, - 3) (D) (4, \frac{1}{2})$

Short Answer

Expert verified

The coordinates of point E is $(7, - 4)$ . So, option (B) is correct.

Step by step solution

Step 1. Write down the given information.

The given segment $\bar{C E}$ has midpoint $D (5, - 1)$ and the point C has coordinates $(3, 2)$ $(3, 2)$ .

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 E say $(h, k)$ can be evaluated by using the midpoint formula.

\begin{matrix} Midpointof \bar{C E} = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ (5, - 1) = (\frac{3 + h}{2}, \frac{2 + k}{2}) \\ 5 = \frac{3 + h}{2}, - 1 = \frac{2 + k}{2} \\ h + 3 = 10, k + 2 = - 2 \\ h = 7, k = - 4 \end{matrix}

Since the point is $E (7, - 4)$ . So, option (B) is correct.

Step 4. Conclusion.

The coordinates of point E is $(7, - 4)$ . So, option (B) is correct.

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Point $D (5, - 1)$ is the midpoint of segment $\bar{C E}$ . If point Chas coordinates $(3, 2)$ then what are the coordinates of point E.
$(A) (8, 1) (B) (7, - 4) (C) (2, - 3) (D) (4, \frac{1}{2})$

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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PointD5,-1is the midpoint of segment CE¯. If point Chas coordinates 3,2then what are the coordinates of point E.A8,1B7,-4C2,-3D4,12

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

Calculus

Mechanics Maths

Probability and Statistics

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Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Point $D (5, - 1)$ is the midpoint of segment $\bar{C E}$ . If point Chas coordinates $(3, 2)$ then what are the coordinates of point E.
$(A) (8, 1) (B) (7, - 4) (C) (2, - 3) (D) (4, \frac{1}{2})$