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AbdurRakib
Joined: 11 May 2014
Last visit: 03 Mar 2026
Posts: 464
Given Kudos: 220
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20 Yale '20 Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
22 Jul 2016, 12:16
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:36) correct
32%
(02:43)
wrong
based on 263
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. (\(\frac{28}{13}\),\(\frac{-56}{13}\))
A. (\(\frac{-40}{7}\),\(\frac{80}{7}\))
B. (-4,8)
C. (-3,6)
D. (\(\frac{11}{5}\),\(\frac{-22}{5}\))
E. (\(\frac{28}{13}\),\(\frac{-56}{13}\))
22 Jul 2016, 13:17
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AbdurRakib
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.
(-4,8)...option B is correct answer.
21 Feb 2019, 18:00
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AbdurRakib
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
Answer: B.
