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# Line l in the xy-plane contains points A and B with coordin

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Kudos [?]: 1117 [0], given: 5159

Line l in the xy-plane contains points A and B with coordin [#permalink]  17 Dec 2017, 14:10
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Question Stats:

62% (01:36) correct 37% (01:08) wrong based on 16 sessions
Line L in the xy-plane contains points A and B with coordinates (-4,5) and (6,-1), respectively. Line k is perpendicular to L and contains the midpoint of line segment AB.

Which of the following statements are true?

Indicate $$all$$ such statements.

A. The slope of line l is -3/5.
B. Line k has a negative slope.
C. Line k contains the point (1,2).
[Reveal] Spoiler: OA

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Joined: 25 Nov 2017
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Kudos [?]: 41 [0], given: 5

Re: Line l in the xy-plane contains points A and B with coordin [#permalink]  18 Dec 2017, 01:48
So we know the coordinates of 2 points on line l and we can calculate the slope of l.
Y2 - Y1 / X2 - X1 = 1 - 5/ 6 - (-4) = -4/10 or -3/5. The slope is negative so answer A is in.
Since k is perpendicular, the slope shoukd be the reciproqual of -3/5 so 5/3 which is positive. B is incorrect.
Finally, we know that line l has a midpoint which is comprised into line k.
We can therefore calculate the coordinates of the mid point : x1+×2 /2 and y1+ y2/2 which gives us (1,2) so choice C is correct.
Amswer A and C

My bad I consider one of the coordinate of the points as negative that is why I had wrong at first

Last edited by Popo on 18 Dec 2017, 18:31, edited 1 time in total.
Moderator
Joined: 18 Apr 2015
Posts: 5567
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Kudos [?]: 1117 [0], given: 5159

Re: Line l in the xy-plane contains points A and B with coordin [#permalink]  18 Dec 2017, 11:53
Expert's post
The OAs are A and C.

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Kudos [?]: 525 [1] , given: 88

Re: Line l in the xy-plane contains points A and B with coordin [#permalink]  08 Feb 2018, 01:23
1
KUDOS
we can take out the slope of a line if we know the coordinates of two points in a plane
Here we have the two points$$(-4,5) and (6,-1)$$
slope is given by $$\frac{y2 - y1}{x2 - x1}$$
slope = $$\frac{-1 - 5}{6- (-4)}$$ = $$\frac{-3}{5}$$
Hence option A is correct

For two perpendicular lines there slope should multiply to $$-1$$
For one line we have a slope i.e already -ve so the slope of the second line cannot be negative or else they will multiply to a +ve number
Hence option B is incorrect

Also we know that line k passes through the midpoint of line L

Use the mid-point formula to get $$x = \frac{x1+x2}{2},y=\frac{y1+y2}{2}$$
$$\frac{-4 + 6}{2},\frac{5+ -1}{2}$$
This simplifies to $$(1,2)$$
Hence option C is correct
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: Line l in the xy-plane contains points A and B with coordin   [#permalink] 08 Feb 2018, 01:23
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