Question

M is the midpoint of CD. C has coordinates (-1, -1) and

M has coordinates (3, 5). Find the coordinates of D.
o (-5, -7)
O (4, 6)
O (6, 10)
0 (7, 11)

Answer 1

(7, 11)

Explanation:

If a line segment has endpoints at A(
`x_1,y_1`) and B(
`x_2,y_2`), the coordinates of the midpoint O(x, y) of the segment AB is given by the formula:

`x=(x_1+x_2)/(2)\\\\y=(y_1+y_2)/(2)`

Given the midpoint M(3, 5) of the segment CD with the coordinates of C at (-1, -1). Let the coordinates of D be at (
`x_2,y_2`). Hence:

`x=(x_1+x_2)/(2)\\\\ 3=(-1+x_2)/(2) \\\\6=-1+x_2\\\\x_2=6+1\\\\x_2=7\\\\y=(y_1+y_2)/(2)\\\\ 5=(-1+y_2)/(2) \\\\10=-1+y_2\\\\y_2=10+1\\\\y_2=11`

Hence the coordinates of D is at (7, 11)