In a rectangular coordinate system, which of the following

Question

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)

Bunuel · Accepted Answer

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} . Answer: A. For more on these issues check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html Hope it helps.

BrentGMATPrepNow · Answer

One approach is to first find the slope
Slope = (18 - 6)/(21 - 5) = 12/16 =  3 / 4

IMPORTANT: if the slope is  3 / 4 , then we can start at (5,6) and move up  3  spaces and then move right  4  spaces to find other points on the line (with INTEGER values)

Start at: (5,6)
Move  3  units up and  4  units to the right to get to the point (9,9) (check answer choices - it's there!)

Answer: A

Cheers ,
Brent

ankitranjan · Answer

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.

GSBae · Answer

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.

KrishnakumarKA1 · Answer

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

ScottTargetTestPrep · Answer

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!

Answer: A

santro789 · Answer

Can someone solve this using graph?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a rectangular coordinate system, which of the following

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a rectangular coordinate system, which of the following

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards