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) $( 5,6 )$
B) $( 5 , - 6 )$
C) $( - 5 , - 4 )$
D) $( - 3 , - 5 )$
E) $( - 5,6 )$

Question

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) $( 5,6 )$
B) $( 5 , - 6 )$
C) $( - 5 , - 4 )$
D) $( - 3 , - 5 )$
E) $( - 5,6 )$

Quizplus · Accepted Answer

We can use the midpoint formula to solve the problem:
Midpoint formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
Since $M(3,4)$ is the midpoint of segment $AB$, the midpoint formula gives us:
$$(\frac{1+x}{2},\frac{2+y}{2}) = (3,4)$$
Simplifying, we get:
$$\frac{1+x}{2} = 3 \longrightarrow x = 5$$
$$\frac{2+y}{2} = 4 \longrightarrow y = 6$$
Therefore, point $B$ has coordinates $(5,6)$, which is answer choice $\boxed{	extbf{(A)}}$

If M(3, 4) Is the Midpoint of the Line Segment (5,6)( 5,6 )(5,6)

If M(3, 4) Is the Midpoint of the Line Segment $( 5,6 )$