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# Happy Thanksgiving but I need some math help

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A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = (\frac{1}{3})AB$, what are the coordinates for point $C$? Express your answer as an ordered pair.

Nov 24, 2017

#1
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A line segment starting at point A(2, -2) extends through point B(14, 4) to point C.

If the length from B to C is 1/3rd the length from A to B, what are the coordinates of point C?

The x-distance from A to B is 12 because 14 - 2 = 12.

The y-distance from A to B is 6 because 4 - -2 = 6.

Since 1/3rd of 12 is 4, the x-value of point C must be 4 more than the x-value of point B  --->   14 + 4 = 18.

Since 1/3rd of 6 is 2, the y-value of point C must be 2 more than the y-value of point B  --->   4 + 2 = 6.

Therefore, the coordinates of point C are (18, 6).

Nov 24, 2017

#1
+17747
+3

A line segment starting at point A(2, -2) extends through point B(14, 4) to point C.

If the length from B to C is 1/3rd the length from A to B, what are the coordinates of point C?

The x-distance from A to B is 12 because 14 - 2 = 12.

The y-distance from A to B is 6 because 4 - -2 = 6.

Since 1/3rd of 12 is 4, the x-value of point C must be 4 more than the x-value of point B  --->   14 + 4 = 18.

Since 1/3rd of 6 is 2, the y-value of point C must be 2 more than the y-value of point B  --->   4 + 2 = 6.

Therefore, the coordinates of point C are (18, 6).

geno3141 Nov 24, 2017