Answer:
E = (5, 8)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Given:
[tex]\textsf{Midpoint}=(2,7)[/tex]
[tex]\textsf{Let endpoint }(x_1,y_1)=\textsf{Point D}=(-1,6)[/tex]
[tex]\textsf{Let endpoint }(x_2,y_2)=\textsf{Point E}=(x_E,y_E)[/tex]
Substitute the given values into the equation:
[tex]\begin{aligned}\textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\implies (2, 7) & =\left(\dfrac{x_E-1}{2},\dfrac{y_E+6}{2}\right)\\\end{aligned}[/tex]
Therefore, the x-coordinate of point E is:
[tex]\implies \dfrac{x_E-1}{2}=2[/tex]
[tex]\implies x_E-1=4[/tex]
[tex]\implies x_E=5[/tex]
The y-coordinate of point E is:
[tex]\implies \dfrac{y_E+6}{2}=7[/tex]
[tex]\implies y_E+6=14[/tex]
[tex]\implies y_E=8[/tex]
Therefore, point E is (5, 8).
