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2 years ago

5. Find the point P along the directed line segment from X(-3, 3) to Y(6,-3) that divides

1 answer:

6 0

Consider point P(x,y) such that P, X and Y are collinear,

As vectors

XP = XO + OZ where O(0,0)
XP = OZ - OX
XP= (x,y) - (-3,3)
XP = (x+3, y-3)

Similarly,

PY = (6-x, -3-y)

But XP= 2^PY

[x+3, y-3] = [2(6-x), 2(-3-y)]

Given both vectors are equal, as they go in the same direction, Solve for x and y accordingly:

x+3 = 12 - 2x

x = 3

y-3 = -6-2y

y = -1

Therefore, P(3,-1)

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The x co-ordinate o intersection of line k and n is $\frac{8}{11}$

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Now intersection of line k and n is

put the value of y from eq 3 into eq 2

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or, 11 x - 8 = 0

or 11 x = 8

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Hence The x co-ordinate o intersection of line k and n is $\frac{8}{11}$ Answer

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