Co-ordinate geometry

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pareekbharat86: Master | Next Rank: 500 Posts; Posts: 168; Joined: Thu Nov 01, 2012 7:43 pm; Thanked: 1 times

by pareekbharat86 » Sat Dec 07, 2013 9:34 pm

What are the coordinates of point B in the xy-plane
below?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

OA B

Thanks,
Bharat.

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Source: Beat The GMAT — Problem Solving | Sat Dec 07, 2013 9:34 pm

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Sat Dec 07, 2013 11:44 pm

pareekbharat86 wrote:What are the coordinates of point B in the xy-plane
below?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

OA B

Hi Bharat,
Question states that AC = BD

AC is 28
So BD should be 28.

So the point B's Y-axis should be of 28.
Eliminate option, A,C,D
Remaining options are B and E.

another thing what question says is that AB = BC. and angle D makes 90 Degree.
therefore, AD should be equal to DC
So only option match is B.
So that AD = DC = 14.

Hence Answer is B

Regards,
Uva.

Known is a drop Unknown is an Ocean

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 08, 2013 8:16 am

pareekbharat86 wrote:What are the coordinates of point B in the xy-plane below?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

If AB= BC, then âˆ†ABC is an ISOSCELES triangle, which mean that BD (the altitude) is also a perpendicular BISECTOR.
If BD bisects AC, then AD = DC
Since AC = 28, we know that AD = DC = 14, which means point D has coordinates (6, 0), which means point B has coordinates (6, ?)

At this point, we can eliminate answer choices C, D and E.
This means that the length of BD is either 12 or 28

IMPORTANT: In official GMAT Problem Solving questions, the given diagrams are drawn to scale unless it is stated otherwise. To learn more about this, you can watch this free video: https://www.gmatprepnow.com/module/gmat-geometry?id=863

So, if this were an official GMAT question, then we could probably just "eyeball" the diagram and determine whether BD has length 12 or 28. This diagram, however, is obviously not drawn to scale, so there should be some wording added to indicate this.

To determine the length of BD, we'll use the fact that BD = AC
Since AC has length 28, we know that BD has length 28, which means point B has coordinates [spoiler](6, 28)[/spoiler]

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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