# geometry

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A point p(x,y) is on the line through A(-4,4) and B(5,2).Find (a) the coordinates of P given that the segment AB is extended through B to P so that P is twice as far from A as far from B,and (b) the coordinates of P given that AB is extended through A to P so that P is three times as far from B as from A.

• geometry -

a. A(-4,4), (B(5,2), P(x,y).

AP = 2BP,
x-(-4) = 2(x-5),
x + 4 = 2x -10,
2x -x = 4 + 10 = 14,
X = 14.

y -4 = 2(y-2),
y -4 = 2y -4,
2y - y = -4 + 4 = 0,
Y = 0.

Solution set: P(14,0).

b. P(x,y), A(-4,4), B(5,2).

PB = 3PA,
5 - x = 3(-4 -x),
5 - x = -12 -3x,
-x + 3x = - 12 - 5,
2x = - 17,
X = -17/2 = -8 1/2.

2 - y = 3(4-y),
2 - y = 12 - 3y,
- y + 3y = 12 - 2,
2y = - 10,
Y = 5

Solution set: P(-8 1/2,5).

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