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

Question

3 years ago

15

midpoint formula and show ALL work. DO NOT use Desmos.

1 answer:

Korvikt [17] · Answer 1 · 2022-03-22T01:55:39+03:00

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)

Learn more about dividing segments:

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