 It is currently 15 Jul 2019, 14:15 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Line l in the xy-plane contains points A and B with coordin  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 7311
Followers: 122

Kudos [?]: 1427 , given: 6561

Line l in the xy-plane contains points A and B with coordin [#permalink]
Expert's post 00:00

Question Stats: 68% (01:27) correct 31% (01:08) wrong based on 19 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

_________________
Manager Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 43 , given: 5

Re: Line l in the xy-plane contains points A and B with coordin [#permalink]
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.
Founder  Joined: 18 Apr 2015
Posts: 7311
Followers: 122

Kudos [?]: 1427 , given: 6561

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

Regards
_________________ Director  Joined: 07 Jan 2018
Posts: 659
Followers: 7

Kudos [?]: 615  , given: 88

Re: Line l in the xy-plane contains points A and B with coordin [#permalink]
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
_________________

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
Display posts from previous: Sort by

# Line l in the xy-plane contains points A and B with coordin  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.