SOLUTION: A line passes through A(2,-2) and B(-4,3). Find the coordinates of the point on the line twice as far from A as from B (show two cases).

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Question 1188642: A line passes through A(2,-2) and B(-4,3). Find the coordinates of the point on the line twice as far from A as from B (show two cases).
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A line passes through A(2,-2) and B(-4,3). Find the coordinates of the point on the line twice as far from A as from B (show two cases).
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(x,y) is a point twice as far from A as from B
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Distance from A = sqrt%28%28x-2%29%5E2+%2B+%28y%2B2%29%5E2%29
Distance from B = sqrt%28%28x%2B4%29%5E2+%2B+%28y-3%29%5E2%29
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%28x-2%29%5E2+%2B+%28y%2B2%29%5E2+=+4%2A%28%28x%2B4%29%5E2+%2B+%28y-3%29%5E2%29
x%5E2+-+2x+%2B+4+%2B+y%5E2+%2B+2y+%2B+4+=+4x%5E2+%2B+32x+%2B+64+%2B+y%5E2+-+6y+%2B+9
-3x%5E2+-+34x+-+60+%2B+8y+-+5+=+0
3x%5E2+%2B+34x+%2B+65+=+8y
y+=+%283%2F8%29x%5E2+%2B+%2817%2F4%29x+%2B+65%2F8
At x = 0, y = 65/8 ---> (0,65/8)
At x = -2, y = 9/8 --> (-2,1.125)