Question

5. Mis the midpoint of CD. C has coordinates (-1,-1) and
M has coordinates (3,5). Find the coordinates of D.

Answer 1

Answer/Step-by-step Explanation:

4. Midpoint (M) of AB, for A(-2, -3) and B(1, 2) is given as:

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

Let $A(-2, -3) = (x_1, y_1)$

$B(1, 2) = (x_2, y_2)$

Thus:

$M(\frac{-2 + 1}{2}, \frac{-3 + 2}{2})$

$M(\frac{-1}{2}, \frac{-1}{2})$

5. Given M(3, 5) as midpoint of CD, and C(-1, -1),

let $C(-1, -1) = (x_2, y_2)$

$D(?, ?) = (x_1, y_1)$

$M(3, 5) = (\frac{x_1 +(-1)}{2}, \frac{y_1 +(-1)}{2})$

Rewrite the equation to find the coordinates of D

$3 = \frac{x_1 - 1}{2}$ and $5 = \frac{y_1 - 1}{2}$

Solve for each:

$3 = \frac{x_1 - 1}{2}$

$3*2 = \frac{x_1 - 1}{2}*2$

$6 = x_1 - 1$

$6 + 1= x_1 - 1 + 1$

$7 = x_1$

$x_1 = 7$

$5 = \frac{y_1 - 1}{2}$

$5*2 = \frac{y_1 - 1}{2}*2$

$10 = y_1 - 1$

$10 + 1= y_1 - 1 + 1$

$11 = y_1$

$y_1 = 11$

Coordinates of D is (7, 11)