Question

B is the midpoint of AC, E is the midpoint of BD. If A(-9,-4), C(-1,6), and E(-4,-3), find the coordinates of D

Answer 1

Answer:

(-3, -7)

Step-by-step explanation:

Let $(x_{A,}y_{A}),(x_{B},y_{B}),(x_{C,}y_{C}),(x_{D,}y_{D})(x_{E,}y_{E)} \text{be the coordinates of points A, B, C respectively}$

The midpoint coordinates $(x_{M},y_{M})$ of any two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are given by $x_{M}=\frac{(x_{1}+x_{2)}}{2}$ and $y_{M}=\frac{y_{1}+y_{2}}{2}$

Since B is the midpoint of AC

$x_{B}=\frac{(x_{A}+x_{C})}{2}=\frac{(-9+(-1)}{2}=\frac{-9-1}{2}=\frac{-10}{2}=-5$

$y_{B}=\frac{(y_{A}+y_{C})}{2}=\frac{(-4+6)}{2}=\frac{2}{2}=1$

Since E is the midpoint of B and D and we are given the coordinates of E as (-4,-3). it follows that

$x_{E}=\frac{x_{B}+x_{D}}{2} = \frac{-4+x_{D}}{2}$

Therefore

$x_{D}=2x_{E}+4=2(-5)+4=-3$

Similarly

$y_{E}=\frac{y_{B}+y_{D}}{2} = \frac{1+x_{D}}{2}y_{D}=2y_{E}-1=2(-3)-7=-7$