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## 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.

## 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.

Glad you like the videos!

Cheers,

Brent

## 1. Do all lines (distance

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?

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

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.

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

## Can there be situation where

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

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.

## Question link: https:/

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