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Line k passes through the points (6,2) and P and has a slope of − 3/5

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Line k passes through the points (6,2) and P and has a slope of − 3/5  [#permalink]

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22 Jul 2016, 11:16
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Question Stats:

67% (02:32) correct 33% (02:41) wrong based on 78 sessions

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Line k passes through the points (6,2) and P and has a slope of $$\frac{−3}{5}$$ . If the line that passes through the origin and point P has a slope of –2, which of the following are the xy-coordinates for point P ?

A. ($$\frac{-40}{7}$$,$$\frac{80}{7}$$)
B. (-4,8)
C. (-3,6)
D. ($$\frac{11}{5}$$,$$\frac{-22}{5}$$)
E. ($$\frac{28}{13}$$,$$\frac{-56}{13}$$)
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Line k passes through the points (6,2) and P and has a slope of − 3/5  [#permalink]

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22 Jul 2016, 12:17
AbdurRakib wrote:
Line k passes through the points (6,2) and P and has a slope of $$\frac{−3}{5}$$ . If the line that passes through the origin and point P has a slope of –2, which of the following are the xy-coordinates for point P ?

A. ($$\frac{-40}{7}$$,$$\frac{80}{7}$$)
B. (-4,8)
C. (-3,6)
D. ($$\frac{11}{5}$$,$$\frac{-22}{5}$$)
E. ($$\frac{28}{13}$$,$$\frac{-56}{13}$$)

This is how I tried.

Given Line k passes through the points (6,2) and P and has a slope of $$\frac{−3}{5}$$.

Let P be (x2,y2).

slope between (6,2) and (x2,y2) is -3/5.

=> $$\frac{y2-2}{x2-6}$$ = $$\frac{-3}{5}$$. (Here used slope formula )
=> 3x2 + 5y2 -28 = 0 ---eq 1.

Then given line that passes through the origin and point P has a slope of –2.

Again same point P and line passes through origin and slope is -2.

$$\frac{y2-0}{x2-0}$$ = -2.

y2 = -2x2 -- eq 2.

Now sub eq 2 in eq 1 we get 3x2 - 10x2 = 28
=> x2 = -4 and y2 = 8.

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Re: Line k passes through the points (6,2) and P and has a slope of − 3/5  [#permalink]

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21 Feb 2019, 17:00
AbdurRakib wrote:
Line k passes through the points (6,2) and P and has a slope of $$\frac{−3}{5}$$ . If the line that passes through the origin and point P has a slope of –2, which of the following are the xy-coordinates for point P ?

A. ($$\frac{-40}{7}$$,$$\frac{80}{7}$$)
B. (-4,8)
C. (-3,6)
D. ($$\frac{11}{5}$$,$$\frac{-22}{5}$$)
E. ($$\frac{28}{13}$$,$$\frac{-56}{13}$$)

We can let the point P be (x,y).

Since we know the slope of both lines, we have:

Slope of k:

(y - 2)/(x - 6) = -3/5

The second line passes through the origin, so its slope is:

(y - 0)/(x - 0) = -2

y/x = -2

y = -2x

Substituting, we have:

(-2x - 2)/(x - 6) = -3/5

5(-2x - 2) = -3(x - 6)

-10x - 10 = -3x + 18

-7x = 28

x = -4; thus, y = 8

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Re: Line k passes through the points (6,2) and P and has a slope of − 3/5   [#permalink] 21 Feb 2019, 17:00