# What is the distance between the points (10,2) and (14,5)?

Dec 1, 2016

5

#### Explanation:

The distance between the final point locations can be calculated from the “distance formula” for Cartesian Coordinate systems:
d= $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

d= $\sqrt{{\left(10 - 14\right)}^{2} + {\left(2 - 5\right)}^{2}}$ ; d= $\sqrt{{\left(- 4\right)}^{2} + {\left(- 3\right)}^{2}}$
d= sqrt ((16+9)
d= sqrt ((25) = 5

Dec 1, 2016

$5$

#### Explanation:

To find the distance between any two point, we use the distance formula

color(blue)("Distance"=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

We know that

color(orange)((10,2)=(x_1,y_1)

color(orange)((14,5)=(x_2,y_2)

So the distance will be

rarrsqrt(color(black)((14-10)^2+(5-2)^2)

rarrsqrt(color(black)((4)^2+(3)^2)

$\rightarrow \sqrt{\textcolor{w h i t e}{\overline{\textcolor{b l a c k}{16 + 9}}}}$

$\rightarrow \sqrt{\textcolor{w h i t e}{\overline{\textcolor{b l a c k}{25}}}}$

color(green)(rArr5