Question

M is the midpoint of CD. Given the coordinates of one endpoint C(10,-5) and the midpoint M(4, 0), find the coordinates of the other endpoint D of CD.

Answer 1

D(-2, 5).

Explanation:

We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).

And we want to determine the coordinates of D.

Recall that the midpoint is given by:

`\displaystyle M = \left((x_1 + x_2)/(2) , (y_1 + y_2)/(2)\right)`

Let C(10, -5) be (x₁, y₁) and Point D be (x₂, y₂). The midpoint M is (4, 0). Hence:

`\displaystyle (4, 0) = \left((10+x_2)/(2) , (-5+y_2)/(2)\right)`

This yields two equations:

`\displaystyle (x_2 + 10)/(2) = 4\text{ and } (y_2 - 5)/(2) = 0`

Solve for each:

`\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}`

And:

`\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}`

In conclusion, Point D = (-2, 5).