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# In a rectangular coordinate system, which of the following

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Manager
Joined: 22 Sep 2010
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In a rectangular coordinate system, which of the following [#permalink]

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20 Oct 2010, 02:55
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In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Sep 2012, 10:03, edited 1 time in total.
Edited the question.
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Posts: 39662
Re: In a rectangular coordinate system ............ [#permalink]

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20 Oct 2010, 03:05
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pzazz12 wrote:
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?
A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)

The slope of a line passing through the points (5,6) and (21,18) is "rise over run": $$\frac{18-6}{21-5}=\frac{3}{4}$$.

The slope of a line passing through the point (5,6) and one of the points from the answer choice must also be $$\frac{3}{4}$$ (as it's the same lin), so $$\frac{y-6}{x-5}=\frac{3}{4}$$.

Answer choice A works: $$\frac{9-6}{9-5}=\frac{3}{4}$$.

For more on these issues check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In a rectangular coordinate system ............ [#permalink]

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20 Oct 2010, 03:15
pzazz12 wrote:
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?
A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)

Equation of the line connecting the two points,(5,6) and (21,18);

y-6= {(6-18)/(5-21)}(x-5) or , 4y-3x=9

Only ( 9,9) is satisfying the equation.Hence answer is A.

Consider KUDOS if its helpful to u .Thanks.
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Re: In a rectangular coordinate system, which of the following [#permalink]

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14 Aug 2013, 03:44
Bumping for review and further discussion.
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Re: In a rectangular coordinate system, which of the following [#permalink]

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30 Dec 2014, 22:26
I think option D also satisfy equation then why only option A is selected?
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Re: In a rectangular coordinate system, which of the following [#permalink]

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31 Dec 2014, 03:55
saurabhk99 wrote:
I think option D also satisfy equation then why only option A is selected?

How does D fit? Show your work.
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In a rectangular coordinate system, which of the following [#permalink]

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31 Dec 2014, 10:24
I found the equation of the line to be $$y = \frac{3x}{4} + \frac{9}{4}.$$. Then, noticing that 3 of the options had the same value for x and y, I wanted to check at which point on the line the x and y values were equal. So I solved for x:

$$x = \frac{3x}{4} + \frac{9}{4}$$
$$\frac{x}{4} = \frac{9}{4}.$$
$$x = 9.$$

Therefore, (9,9) is a point on the line and our answer is A.

Further: If we would have found some other value (one that wasn't listed on the answer choices) then we at least could have eliminated 3 of the answer choices and then manually checked the other two.
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Re: In a rectangular coordinate system, which of the following [#permalink]

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31 Dec 2014, 17:10
made mistake in calculation....agree A is the right one
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Re: In a rectangular coordinate system, which of the following [#permalink]

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17 Feb 2016, 04:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a rectangular coordinate system, which of the following [#permalink]

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07 Mar 2017, 18:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a rectangular coordinate system, which of the following [#permalink]

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07 Mar 2017, 19:43
A . As the slope of the line calculated from given cordinates matches the slope calculated from option A.

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Re: In a rectangular coordinate system, which of the following [#permalink]

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08 Mar 2017, 02:19
equation of line: y-6 = {(18-6)/(21-5)} (x-5)
rearranging we get 4y-3x = 9. Put the co ordinates, given in the option, in the equation.

we will get (9,9) as answer

Option A
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Re: In a rectangular coordinate system, which of the following [#permalink]

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10 Mar 2017, 10:35
pzazz12 wrote:
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

Let’s first create the equation of a line for coordinates (5,6) and (21,18).

Slope = Δy/Δx = 12/16 = 3/4.

We can substitute in either ordered pair to calculate the y-intercept. Let’s use (5,6):

y = (3/4)x + b

6 = (3/4)(5) + b

6 = 15/4 + b

24/4 = 15/4 + b

9/4 = b

Thus, y = (3/4)x + 9/4

Let’s now substitute each set of coordinates to see which holds true in our equation.

A) (9,9)

9 = (3/4)(9) + 9/4 ?

9 = 27/4 + 9/4 ?

9 = 36/4 ?

9 = 9 ? → Yes!

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Re: In a rectangular coordinate system, which of the following   [#permalink] 10 Mar 2017, 10:35
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