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

Answer:

(7, 11)

Step-by-step 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:

$x=\frac{x_1+x_2}{2}\\\\y=\frac{y_1+y_2}{2}$

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:

$x=\frac{x_1+x_2}{2}\\\\ 3=\frac{-1+x_2}{2} \\\\6=-1+x_2\\\\x_2=6+1\\\\x_2=7\\\\y=\frac{y_1+y_2}{2}\\\\ 5=\frac{-1+y_2}{2} \\\\10=-1+y_2\\\\y_2=10+1\\\\y_2=11$

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