Question

Line segment DG contains the point D(-2,3) and a midpoint at O(3,-1.5) what is the location of endpoint G

Answer 1

To solve this we will use the midpoint formula. The midpoint formula states that:

The midpoint of two points, $(x_1, y_1)$ and $(x_2, y_2)$ is the point O found by the following formula:

x coordinate of O: $\frac{x_1+x_2}{2}$

y coordinate of O: $\frac{y_1+y_2}{2}$

Now, let us apply this formula in our question to find the location of the enpoint G. In our case the mid point is already given as O(3,-1.5). Thus, the x coordinate of O is 3 and the y coordinate of O is -1.5.

Also, $x_1=-2$ and

$y_1=3$

Applying the formula we will get two sets of equations. The first one will be:

$\frac{-2+x_2}{2}=3$

Therefore, $x_2-2=3\times 2=6$

$x_2=6+2=8$

Likewise, we can find the $y_2$ as:

$\frac{3+y_2}{2}=-1.5$

$3+y_2=-3$

$y_2=-6$

Thus, the location of the endpoint G is (8,-6)

Please find the attached file to get a complete picture of the solution of this question.

Answer 2

3= (-2+X)/2
6=-2+X
8=x

3=(1.5+Y)/2
6=1.5+Y
4.5=Y

G=(8,4.5)