# Lesson: Distance Between Two Points

## Comment on Distance Between Two Points

### Hey Brent,

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

### Sticking with the Pythagorean

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

Cheers,
Brent

### 1. Do all lines (distance

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.

Thanks!

### 1. Any time the line is

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 :-)

Cheers,
Brent

### How can an line be determined

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

Thank you!

### If two points on a line share

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.

### Can there be situation where

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.

### The formula for finding the

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.

Cheers,
Brent

### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-x-3-which-of-the-following-must-be-true-138652.html
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.

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

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?

### Is this the question you're

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