coordinate problem

**zelda1850** · April 22nd 2010, 04:28 PM

the coordinate of the midpoint of a line segement AB are (-2,4) if the coordinate of point A are (7,10) what are the coordinates of B?

how can i solve this problem i tried using the midpoint formula but it doesnt work

**Archie Meade** · April 22nd 2010, 04:46 PM

Originally Posted by zelda1850

the coordinate of the midpoint of a line segement AB are (-2,4) if the coordinate of point A are (7,10) what are the coordinates of B?

how can i solve this problem i tried using the midpoint formula but it doesnt work

Hi zelda,

the midpoint formula ought to work easily enough.

You can simply say....

the x co-ordinate of the midpoint is halfway between the x co-ordinates
of the points on the line.

So -2 is halfway between 7 and another x.
-2 is 9 away from 7.
The other value 9 away from -2 is -11.

So -2 is halfway between -11 and 9.

Also 4 is halfway between 10 and -2

The other point is (-11,-2).

Using the midpoint formula, which is

"the x midpoint is the average of the x values"
"the y midpoint is the average of the y values".

$\frac{x_1+x_2}{2}=-2$

$x_1+x_2=-2(2)=-4$

$x_1=-4-x_2=-4-7=-11$

$\frac{y_1+y_2}{2}=4$

$y_1+y_2=4(2)=8$

$y_1=8-y_2=8-10=-2$

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