Question

Point K is the midpoint of QZ. Point K is located at (-1,-11), and point Z is located at (7,-3). Where is point Q located?

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{7+x}{2}~~,~~\cfrac{-3+y}{2} \right)~~=~~\stackrel{\stackrel{midpoint}{K}}{(-1,-11)}\implies \begin{cases} \cfrac{7+x}{2}=-1\\[1em] 7+x=-2\\ \boxed{x=-9}\\ \cline{1-1} \cfrac{-3+y}{2}=-11\\[1em] -3+y=-22\\ \boxed{y=-19} \end{cases}$

Answer 2

Answer:

$(-9,-19)$

Step-by-step explanation:

Givens

$K(-1,-11)\\Z(7,-3)\\Q(x_{1},y_{1})$

Now, the definition of midpoint is

$K(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2}}{2} )$

But, we know that $K(-1,-11)$, so we replace each vale, where $x_{2} =7$ and $y_{1}=-3$

$-1=\frac{x_{1}+7 }{2} \\-2=x_{1}+7\\-2-7=x_{1}\\x_{1}=-9$

$\frac{y_{1}+y_{2}}{2}=-11\\y_{1}-3=-22\\y_{1}=-22+3\\y_{1}=-19$

Therefore, Q is located at $(-9,-19)$