Question

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

Answer 1

5

Explanation:

The distance between the final point locations can be calculated from the “distance formula” for Cartesian Coordinate systems:
d= `sqrt ((x_2-x_1)^2+(y_2-y_1)^2)`

d= `sqrt ((10 - 14)^2+(2 - 5)^2)` ; d= `sqrt ((-4)^2+(-3)^2)`
d= `sqrt ((16+9)`
d= `sqrt ((25)` = 5

Answer 2

`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)`

`rarrsqrt(color(white)(barcolor(black)(16+9)))`

`rarrsqrtcolor(white)(barcolor(black)(25))`

`color(green)(rArr5`