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i need help. i'm just confused - division of a line segment (analytic geom - gordon fuller)

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I'm confused if I'm going to use 1/3 or 3 as r in the problem.please help me!! :((

A line passes through A(-2,-1) and B(3,4). Find (a) the pointP on line AB extended through B so that P is three times asfar from A as from B; (b) the point, if P is on line AB extendedthrough A so that P is three times as far from B as from A.

Algebra

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Anonymous - 2 hours later

y = m*x + b

m = 5/5 = 1

y = x + b

4 = 3 + b <=> b = 1

So, f(x) = y = x + 1

Since the slope is 1, if we divide the interval [-2,3] we cananswer your question.

a) 2 * 5 (length of the interval) * (3/4) (so that the point inquestion is three times as far from A asfrom B) = 1.75

The point is (1.75, f(1,75)) = (1.75, 2.75)

Confirmation:

Distance from A:

√((1.75 + 2)^2 + (2.75 + 1)^2) = 5.3033

Distance fromB:

√((1.75 - 3)^2 + (2.75- 4)^2) ˜ 1.76777

b) -2 * 5 (length of the interval) * (1/4) (so that the point inquestion is three times as far from B asfrom A) = -0.75

The point is (-0.75, f(-0,75)) = (-0.75, 0.25)

Confirmation:

Distance fromA:

√((-0.75 + 2)^2 +(0.25 + 1)^2) ˜ 1.76777

Distance fromB:

√((-0.75 - 3)^2 +(0.25 - 4)^2) = 5.3033