# Question 78376

Jan 10, 2018

Coordinates of $Y a r e \textcolor{red}{- 4 , 7}$

#### Explanation:

Given $X \left(4 , 5\right) , M \left(0 , 6\right)$ and M is the midpoint of X & Y.

To find Y

${M}_{x} = \frac{{X}_{x} + {Y}_{x}}{2}$

${Y}_{x} = 2 {M}_{x} - {X}_{x} = \left(2 \cdot 0\right) - 4 = - 4$

Similarly,
Y_y = 2M_y - X_y = (2*6) - 5) = 7#

Coordinates of $Y a r e \textcolor{red}{- 4 , 7}$

Jan 10, 2018

$Y \left(- 4 , 7\right)$

#### Explanation:

$\text{M is the midpoint of XY}$

$\Rightarrow \vec{X M} = \vec{M Y}$

$\Rightarrow \underline{m} - \underline{x} = \underline{y} - \underline{m}$

$\Rightarrow \underline{y} = 2 \underline{m} - \underline{x}$

$\textcolor{w h i t e}{\Rightarrow \underline{y}} = 2 \left(\begin{matrix}0 \\ 6\end{matrix}\right) - \left(\begin{matrix}4 \\ 5\end{matrix}\right)$

$\textcolor{w h i t e}{\Rightarrow \underline{y}} = \left(\begin{matrix}0 \\ 12\end{matrix}\right) - \left(\begin{matrix}4 \\ 5\end{matrix}\right) = \left(\begin{matrix}- 4 \\ 7\end{matrix}\right)$

$\Rightarrow Y = \left(- 4 , 7\right)$