Question

The midpoint of overline PQ is M = (- 2, 1) . One endpoint is P = (- 5, - 1) Find the coordinates of the other endpoint , Q.

Answer 1

Answer;

The coordiantes of the point Q is;

`(1,3)`

Explanation;

Here, we want to get the coordinates of the other endpoint

Mathematically, we can find the midpoint of two endpoints using the formula below;

`(x,y)\text{ = (}((x_1+x_2))/(2),((y_1+y_2))/(2))`

The notation 1 and 2 represents the coordinates of the two end points

Now, by replacing the values given in the question, we have it that;

(x,y) is the coordinate of the point m which is (-2,1)

Now the first end point has the coordinates (-5,-1)

The second endpoint Q has the endpoint (x2,y2) which we want to calculate

We proceed to make the substitutions as follows;

`(-2,1)\text{ =}((-5+x_2))/(2),((-1+y_2))/(2)`

We proceed to susbtitute the individual branches as follows;

`\begin{gathered} -2\text{ = }(-5+x_2)/(2) \\ 2(-2)=-5+x_2 \\ -4=-5+x_2 \\ x_2=-4+5 \\ x_2\text{ = 1} \end{gathered}`

Finally, we have;

`\begin{gathered} 1=(-1+y_2)/(2) \\ 2(1)=-1+y_2 \\ 2+1=y_2 \\ y_2\text{ = }3 \end{gathered}`