Question

Midpoint of DE is M(2,7)
D(-1,6), E(____,_____)

Answer 1

• E(5, 8)

Explanation:

Let E has coordinates of x and y.

Use midpoint equation to find x and y:

• 2 = 1/2( - 1 + x) ⇒ 4 = - 1 + x ⇒ x = 4 + 1 ⇒ x = 5
• 7 = 1/2(6 + y) ⇒ 14 = 6 + y ⇒ y = 14 - 6 ⇒ y = 8

Answer 2

E = (5, 8)

Explanation:

Midpoint between two points

`\textsf{Midpoint}=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)`

Given:

`\textsf{Midpoint}=(2,7)`

`\textsf{Let endpoint }(x_1,y_1)=\textsf{Point D}=(-1,6)`

`\textsf{Let endpoint }(x_2,y_2)=\textsf{Point E}=(x_E,y_E)`

Substitute the given values into the equation:

`\begin{aligned}\textsf{Midpoint} & =\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\\\implies (2, 7) & =\left((x_E-1)/(2),(y_E+6)/(2)\right)\\\end{aligned}`

Therefore, the x-coordinate of point E is:

`\implies (x_E-1)/(2)=2`

`\implies x_E-1=4`

`\implies x_E=5`

The y-coordinate of point E is:

`\implies (y_E+6)/(2)=7`

`\implies y_E+6=14`

`\implies y_E=8`

Therefore, point E is (5, 8).