SOLUTION: The line segment joining points A(4,6) and B(-1,-2) is extended through A by three times its original length. Find the coordinates of the new endpoint.

Question 936165: The line segment joining points A(4,6) and B(-1,-2) is extended through A by three times its original length. Find the coordinates of the new endpoint.

Found 2 solutions by TimothyLamb, lwsshak3:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
slope = m = dy/dx
m = (6+2)/(4+1)
m = 8/5
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3m = 24/15
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new point C, extended through A(4,6):
C = (4+15,6+24)
C = (19,30)
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check:
m = (30-6)/(19-4)
m = 24/15
m = (8*3)/(5*3)
m = 8/5
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answer:
C(19,30)
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Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The line segment joining points A(4,6) and B(-1,-2) is extended through A by three times its original length. Find the coordinates of the new endpoint.
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The line segment joining given points (4,6) and (-1-2) is the hypotenuse of a right triangle with legs of 5 and 8. By extending the line segment(hypotenuse) 3 times its original length, another larger right triangle is formed which is proportional to the smaller right triangle with given line segment. Since we are extending the hypotenuse of the smaller triangle, the legs are similarly extended 3 times their original length.
..
The x-coordinate (4) is extended by 15(3 times 5)
The y-coordinate (6) is extended by 24(3 times 8)
Coordinates of the new endpoint:(19,30)
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