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((x_1 + x_2)/(2), (y_1 + y_2)/(2))`

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

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

Thus:

`M((-2 + 1)/(2), (-3 + 2)/(2))`

`M((-1)/(2), (-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) = ((x_1 +(-1))/(2), (y_1 +(-1))/(2))`

Rewrite the equation to find the coordinates of D

`3 = (x_1 - 1)/(2)` and
`5 = (y_1 - 1)/(2)`

Solve for each:

`3 = (x_1 - 1)/(2)`

`3*2 = (x_1 - 1)/(2)*2`

`6 = x_1 - 1`

`6 + 1= x_1 - 1 + 1`

`7 = x_1`

`x_1 = 7`

`5 = (y_1 - 1)/(2)`

`5*2 = (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)