Question

M (-4, 8) is the midpoint of line segment DE. D has coordinates (6,1). Find the coordinates of E.

Answer 1

Answer on Question #34567 – Math – Analytic Geometry

Question

M (-4, 8) is the midpoint of line segment DE. D has coordinates (6,1). Find the coordinates of E.

Solution

Suppose that E has coordinates $(x, y)$. Because M is the midpoint of the segment DE then

$$\left\{ \begin{array}{l} -4 = \frac{6 + x}{2}, \\ 8 = \frac{1 + y}{2}, \end{array} \right. \Rightarrow \left\{ \begin{array}{l} -8 = 6 + x, \\ 16 = 1 + y, \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = -14, \\ y = 15. \end{array} \right.$$

Answer:

E has coordinates $(-14, 15)$.

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