Distance between two points A and B whose coordinates are (a, 2) and

Question

Distance between two points A and B whose coordinates are (a, 2) and (4, 6) is 5 units. What is the value of ‘a’?

(A) 0
(B) 1 
(C) 7 
(D) 1 or 7 
(E) Cannot be determined

Parthadhikari · Answer

D. 
a-4 is +-3 using distance formula in coordinate geometry.

Posted from my mobile device

Abhishek009 · Answer

5^2 = ( 6 - 2 )^2 + (4 - a)^2

Or,  25 = 16 + (4 - a)^2

Or,  (4 - a) = +3  or  -3

Thus,  a = 1  or  7 , Answer must be (D)

Jainam24 · Answer

Have attached the solution below 
Ans is Option D

mikemcgarry   VeritasKarishma   chetan2u  ,could you please help explain how I could use the rise over run method to find 7 as one of the answers. I tried a bit but could not figure out thus inevitably had to solve through distance formula. Thanks in advance.

KarishmaB · Answer

Rise/Run is the slope of a line. We are not given the slope here. 
We are given the distance between two points. 
The distance is 5 which reminds us of pythagorean triplet 3-4-5 because all given co-ordinates are integers.

Since the vertical distance between (a, 2) and (4, 6) is 4 ( = 6 - 2), we know that the horizontal distance must be 3. Hence a will be 3 steps to the left of 4 or 3 steps to the right of 4. Hence a will be either 1 or 7.

Distance between two points A and B whose coordinates are (a, 2) and

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

Distance between two points A and B whose coordinates are (a, 2) and

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