Answer:
D(-2, 5).
Step-by-step 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:
[tex]\displaystyle M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)[/tex]
Let C(10, -5) be (x₁, y₁) and Point D be (x₂, y₂). The midpoint M is (4, 0). Hence:
[tex]\displaystyle (4, 0) = \left(\frac{10+x_2}{2} , \frac{-5+y_2}{2}\right)[/tex]
This yields two equations:
[tex]\displaystyle \frac{x_2 + 10}{2} = 4\text{ and } \frac{y_2 - 5}{2} = 0[/tex]
Solve for each:
[tex]\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}[/tex]
In conclusion, Point D = (-2, 5).
