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# The midpoint of the line segment between $(x,y)$ and $(-9,1)$ is $(3,-5)$. Find $(x,y)$.

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The midpoint of the line segment between $(x,y)$ and $(-9,1)$ is $(3,-5)$. Find $(x,y)$.

Nov 22, 2017

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Use the midpoint formula to get you started and then work from there!

The midpoint formula tells you to find the average of the x-coordinates and y-coordinates.

$$(\frac{x-9}{2},\frac{y+1}{2})$$Now that we have the expression for both the x- and y-coordinate, solve for the individual variables.
 $$\frac{x-9}{2}=3$$ $$\frac{y+1}{2}=-5$$

Multiply both equations by 2 to eliminate the fraction.
 $$x-9=6$$ $$y+1=-10$$

Subtract the constant to isolate the variable.
 $$x=15$$ $$y=-11$$

$$(15,-11)$$This is the coordinate.

Nov 22, 2017
edited by TheXSquaredFactor  Nov 22, 2017

#1
+2

Use the midpoint formula to get you started and then work from there!

The midpoint formula tells you to find the average of the x-coordinates and y-coordinates.

$$(\frac{x-9}{2},\frac{y+1}{2})$$Now that we have the expression for both the x- and y-coordinate, solve for the individual variables.
 $$\frac{x-9}{2}=3$$ $$\frac{y+1}{2}=-5$$

Multiply both equations by 2 to eliminate the fraction.
 $$x-9=6$$ $$y+1=-10$$

Subtract the constant to isolate the variable.
 $$x=15$$ $$y=-11$$

$$(15,-11)$$This is the coordinate.

TheXSquaredFactor Nov 22, 2017
edited by TheXSquaredFactor  Nov 22, 2017