If M(3, 4) is the midpoint of the line segment AB, and if A has coordinates (1, 2), find the coordinates of B
A) (-3, -5)
B) (-5, 6)
C) (-5, -4)
D) (5, 6)
E) (5, -6)

Question

Quizplus · Accepted Answer

Using the midpoint formula, we have:
$$M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$
Plugging in the given values, we get:
$$3 = \frac{1+x_2}{2} \Rightarrow x_2 = 5$$
$$4 = \frac{2+y_2}{2} \Rightarrow y_2 = 6$$
Therefore, B has coordinates (5, 6), which corresponds to choice D.

If M(3, 4) Is the Midpoint of the Line Segment