# What is the distance between #(1,-4)# and #(7,5)#?

##### 3 Answers

#### Explanation:

make a right angle triangle with the two points being the end points of the hypotenuse.

The distance between the

The distance between the

So our triangle has two shorter sides 6 and 9 and we need to find the length of the hypotenuse, use Pythagoras.

#### Explanation:

#"calculate the distance d using the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(1,-4)" and "(x_2,y_2)=(7,5)#

#d=sqrt((7-1)^2+(5-(-4))^2)#

#color(white)(d)=sqrt(6^2+9^2)=sqrt(36+81)=sqrt117~~10.82#

#### Explanation:

If you were to draw a right triangle so that the hypotenuse is the line between

where

Solving for the length of the hypotenuse (i.e. the distance between the points

The process of finding the distance between two points by use of a right triangle can be formulated thusly:

Distance

This is called the distance formula, and can be used to expedite the solving of this sort of problem.