Question

What is the distance between the points (-4, 6) and (1, -6)?

Answer 1

The distance between these 2 points is 13.

Explanation:

Picture the 2 points on a graph as a right triangle, where the hypotenuse of that right triangle is the distance between the points. It is very easy to find the length of the legs of that triangle, and you can use those legs to calculate the length of the hypotenuse.

First, find the vertical distance, or the distance between the y-coordinates. Either just look at a graph and count, or subtract them.

`-6-6=-12`

Distance is an absolute value from 0, so -12 is the same as 12.

Next, find the horizontal distance between the x-coordinates.

`1--4=5`

Now, we have the length of the legs, 5 and 12. Use the pythagorean theorem to find the length of the hypotenuse:

`a^2+b^2=c^2\\5^2+12^2=c^2\\25+144=c^2\\c^2=169\\c=√(169)\\c=13`

The distance between these 2 points is 13.