Question

3. Point A is located at (3,6). The midpoint of line segment AB is point C(11,13). What are the coordinates of point B? Use the midpoint formula and show ALL work. DO NOT use Desmos.

Answer 1

Coordinates of point B are (19,20)

Step-by-step explanation:

The midpoint of a segment is located exactly halfway between the two ends of the segment.

Given a segment AB with endpoints with coordinates:

$A(x_A,y_A)\\B(x_B,y_B)$

Then the coordinates of the midpoint C are given by

$C(x_C,y_C)=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})$ (1)

In this problem, we know:

A (3,6)

C (11,13)

Therefore we need to find the coordinates of B. We can do it by re-arranging the equations (1):

$x_C=\frac{x_A+x_B}{2}\rightarrow x_B=2x_C-xA$

And substituting,

$x_B=2(11)-3=19$

Similarly, for the y-coordinate,

$y_B=2y_C-y_A=2(13)-6=20$

Therefore the coordinates of point B are

B (19,20)

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