The coordinates of point R are [tex](-10,12)[/tex].
Given:
M is the midpoint of QR.
To find:
The coordinates of point R.
Explanation:
Midpoint formula: The midpoint of a line segment whose endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
[tex]\text{Midpoint}=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Let [tex](a,b)[/tex] be the coordinates of point R.
Using the midpoint formula, we get
[tex]M=\left(\dfrac{-4+a}{2},\dfrac{6+b}{2}\right)[/tex]
[tex](-7,9)=\left(\dfrac{-4+a}{2},\dfrac{6+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-4+a}{2}=-7[/tex]
[tex]-4+a=-14[/tex]
[tex]a=-14+4[/tex]
[tex]a=-10[/tex]
And,
[tex]\dfrac{6+b}{2}=9[/tex]
[tex]6+b=18[/tex]
[tex]b=18-6[/tex]
[tex]b=12[/tex]
Therefore, the coordinates of point R are [tex](-10,12)[/tex].
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