Coordinate Geometry Question

Expert replies

Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sat Aug 20, 2016 9:23 am

Point (1,0) is closest to which of the following lines?

A. y=x
B. y=1
C. y+x=3
D. x=2
E. x+y=âˆ’1

How to approach this question??

Like this post

Source: Beat The GMAT — Problem Solving | Sat Aug 20, 2016 9:23 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Aug 20, 2016 6:01 pm

Hi Mo2men,

You might find it helpful to graph the 5 answer choices (it shouldn't take too much effort), so that you can physically 'see' how close (1,0) is to each line. Once you can see the lines, you should notice certain patterns - such that (1,0) is the same distance away from Answer B and Answer D (so neither of those can be the correct answer).

If you take that approach, which answer would you choose?

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Aug 20, 2016 6:02 pm

I would start by seeing roughly how close the lines are to that point. Probably most of them could be eliminated by comparing them that way. Then, if more than one are left, get more technical and exact, if necessary.

(A) Closest integer points are (0,0) and (1,1). Those two are each 1 away from (1,0). This line has a slope of 1 and rises at a 45 degree angle. Between those two integer points is a spot on the line that is diagonally closer than 1 away from (1,0).

So < 1.

(B) The closest point on this line is (1, 1). It's 1 away from (1, 0), and as soon as we move to the left or right of it we go further from (1, 0).

So = 1, and A is closest so far.

(C) This is the same as y = -x + 3.

When y = 0, x = 3. (3, 0) is 2 away from (1,0).

When x = 1, y = 2. That's also 2 away from (1,0).

There is a closer point between those two points, but since y = -x + 3 has a slope of -1, it is a 45 degree line, like y = x, and y = x is only one away at integer points. So A is still closer.

(D) x = 2 is 1 away at its closest point, (2,0), similarly to how y = 1 is.

A is still winning.

(E) y = -x - 1.

When x = 1, y = -2, 2 away from (1,0).

When y = 0, x = -1, 2 away from (1,0).

So, like the line in C, this has a 45 degree or - 1 slope, and passes further way than y = x.

So there was no need to get very technical or calculate the exact distances.

A wins.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Aug 21, 2016 2:38 am

Mo2men wrote:Point (1,0) is closest to which of the following lines?

A. y=x
B. y=1
C. y+x=3
D. x=2
E. x+y=âˆ’1

I received a PM requesting that I comment.

Many coordinate plane problems can be solved by DRAWING.
To plot a non-vertical, non-horizontal line:
1. Determine the y-intercept by plugging in x=0 and solving for y.
2. Determine the x-intercept by plugging in y=0 and solving for x.
3. If necessary, determine an additional point by plugging in x=1 and solving for y.
4. Draw a line through the determined points.

Here are (1,0) and the five lines above:

(1,0) is clearly closest to y=x.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review