star rating Rated 4.7/5 by parents and students
Online school tutoring available now
Join over 6,000 Australian families
Enrol Now
MENU hamburger menu
CLOSE
close menu

PRIMARY

2 - 6

SECONDARY

7 - 10

SENIOR

11 - 12

Home

Distance Formula

Theory & Practice Question.

Lesson

 
Distance formula

[Formula]

d=√(〖(x_2-x_1)〗^2+〖(y_2-y_1)〗^2 )

 

Example

Show that the distance between the two points (8,6) and (4,2) is the same as the distance between the two points (9,4) and (13, 0).

 

Solution

Recall the distance formula

d=√(〖(x_2-x_1)〗^2+〖(y_2-y_1)〗^2 )

Let x1 = 8,   x2 = 4,   y1 = 6,   y2 = 2

d=√(〖(4-6)〗^2+〖(2-6)〗^2 )

 

Repeating the process:

Let x1 = 9,   x2 = 13,   y1 = 4,   y2 = 0

d=√(〖(13-9)〗^2+〖(0-4)〗^2 )

 

Therefore:

d1 = d2

and so the distance between the two sets of points are equal

 

Question

Determine the distance between the points (-5,-7) and (-3,1), simplifying your answer where necessary

 

Explanation

The distance between 2 points (x1, y1) and (x2, y2) is found using the formula

d=√(〖(x_2-x_1)〗^2+〖(y_2-y_1)〗^2 )

 

When applied to the points (-5,-7) and (-3,1), we have

d=√(〖((-3)-(-5))〗^2+〖(1-(-7))〗^2 )

 

Want a FREE question and answer worksheet?

Download Your Free Distance Formula Maths Worksheet With Answers PDF Here >>

Get your personalised program, pronto!

Enter a few details below

School Year