# What is the distance between P(0, 0) and Q(5, 12)?

##### 1 Answer

May 26, 2016

#### Explanation:

The distance between two points can be determined using the distance formula:

#color(blue)(|bar(ul(color(white)(a/a)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)color(white)(a/a)|)))#

In your case, to find the distance between the two given points, let:

#(color(red)(x_1),color(blue)(y_1))=(color(red)0,color(blue)0)# #(color(darkorange)(x_2),color(violet)(y_2))=(color(darkorange)5,color(violet)12)#

With these two points, substitute them into the distance formula.

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#d=sqrt((color(darkorange)5-color(red)0)^2+(color(violet)12-color(blue)0)^2)#

#d=sqrt((5)^2+(12)^2)#

#d=sqrt(25+144)#

#d=sqrt(169)#

#d=color(green)(|bar(ul(color(white)(a/a)color(black)(13)color(white)(a/a)|)))#