Lesson: Distance Between Two Points

Comment on Distance Between Two Points

Hey Brent,

Is it sufficient to stick to the phythagorean theorem? I've already got so many new formulas in my head, so it would be nice to be able to skip the distance formula all together if possible. :D

Thanks for all your helpful videos and replies.
gmat-admin's picture

Sticking with the Pythagorean Theorem is perfectly fine. After all, the distance formula is basically just an extension of the Pythagorean Theorem.

Glad you like the videos!


1. Do all lines (distance between 2 points) create a right triangle?

2. Does the formula 'the square root of (x1-x2) squared + (y1-y2) squared' work for finding the distance between 2 points whether it's a right triangle or not?

3. I believe using the formula (item 2) is better because one does not have to draw and possibly make a mistake in estimating the distance.

Your thoughts, please?

gmat-admin's picture

1. Any time the line is slanted (i.e., the line is neither vertical nor horizontal), we can create a right triangle by adding vertical and horizontal lines.

2. The formula always works.

3. Sounds good to me :-)


How can an line be determined to be 'neither vertical nor horizontal,' or how can a line be identified as 'slanted'?

Thank you!
gmat-admin's picture

If two points on a line share the same y-coordinate, then the line is horizontal.
For example, the line connecting points (1,3) and (6,3) is horizontal.

If two points on a line share the same x-coordinate, then the line is vertical.
For example, the line connecting points (1,3) and (1,7) is vertical.

More on this here: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Can there be situation where we must know that other formula to find the length of a Slant line on X,Y Plain?

Or Pythagorus Theorem will always work in each scenario.
gmat-admin's picture

The formula for finding the distance between two points on the coordinate plane is just an extension of the Pythagoras Theorem.

So, the Pythagoras Theorem will always work.


Hi Brent, in this question, why is |x-1|>2 false? Here x-1>2 and -(x-1)<2. On simplifying we get x>3 and -x<-3, which is the same as the target question |x|>3.
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-3-which-of-the-following-must-be-true-13...

Your first step, -(x-1)<2, is incorrect.

If |x-1|> 2, then we know that: x-1 > 2 OR x-1 < -2 [this is covered at https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid... ]

Take: x-1 > 2
Add 1 to both sides to get: x > 3

Take: x-1 < -2
Add 1 to both sides: x < -1

So, x > 3 OR x < -1

In my mock test, I got something like calculate cube root of a number that is not a exact cube, like (32)^(1/3), how do you calculate that?
gmat-admin's picture

Is this the question you're referring to: https://gmatclub.com/forum/if-m-4-1-2-4-1-3-4-1-4-then-the-value-of-m-is...
If so, here's my solution: https://gmatclub.com/forum/if-m-4-1-2-4-1-3-4-1-4-then-the-value-of-m-is...

Just know that the GMAT will never require you to actually calculate the cube root of a value. You need only determine what two integers the cube root falls between.

For example, let's calculate the approximate value of (32)^(1/3)
We know that (27)^(1/3) = 3 and (64)^(1/3) = 4
Since 32 falls between 27 and 64, we know that (32)^(1/3) falls between 3 and 4.
In other words, (32)^(1/3) = 3.something

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