Question

If M is the midpoint of XY, find the coordinates of X if M(-3,-1) and Y(-8,6)

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) X&({{ a}}\quad ,&{{ b}})\quad % (c,d) Y&({{ -8}}\quad ,&{{ 6}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{-8+a}{2}~,~\cfrac{6+b}{2} \right)=\stackrel{M}{(-3,-1)}\implies \begin{cases} \cfrac{-8+a}{2}=-3\\\\ -8+a=-6\\ \boxed{a=2}\\ ----------\\ \cfrac{6+b}{2}=-1\\\\ 6+b=-2\\ \boxed{b=-8} \end{cases}$

Answer 2

the coordinates of X is (2,-8)

Given :

M(-3,-1) and Y(-8,6)

M is midpoint of XY

Let X be (x1,y1)

Apply mid point formula $(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

(x2,y2) is (-8,6)

Replace the values in the formula

$(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )=(-3,-1)\\(\frac{x_1-8}{2} , \frac{y_1+6}{2} )=(-3,-1)\\\frac{x_1-8}{2}=-3\\x_1-8=-6\\x_1=-6+8\\x_1=2$

Now we find out y1

$\frac{y_1+6}{2}=-1\\y_1+6=-2\\ y_1=-2-6\\y_1=-8$

so the coordinates of X is (2,-8)

Learn more : brainly.com/question/17522586