 # Finding the Length of a Line Segment

In this worksheet, students find the length of a line segment, given the coordinates of its endpoints. Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Difficulty level:   ### QUESTION 1 of 10

Given the coordinates of the endpoints of a line segment, we can use Pythagoras' Theorem to find its length.

A right-angled triangle is needed.

The x-part of the right-angled triangle will be the difference of the x-coordinates of each endpoint.

The y-part of the right-angled triangle will be the difference of the y-coordinates of each endpoint.

Example

Find the length of the line segment whose endpoints are at (-4, -3) and (2, 4)

Answer

The x-part is the difference between -4 and 2, which is is -4 - 2 = -6, so we use 6 as the distance.

The y-part is the difference between -3 and 4, which is is -3 - 4 = -7, so we use 7 as the distance.

This is shown in the diagram below, where the length of the line segment is marked as d. Using Pythagoras' Theorem, we get:

d2 = 62 + 72

d2 = 36 + 49 = 85

d = √85 = 9.22 units

Find the length of the line segment whose endpoints are at:

(4, 0) and (2, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(4, 0) and (1, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(4, 3) and (7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(4, -3) and (7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(-4, 0) and (-7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(14, -3) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(4, -3) and (-4, 3)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(14, 20) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(14, -20) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

Find the length of the line segment whose endpoints are at:

(12, 26) and (3, -14)

(Give your answer to 3 sig. figs. if it is not an integer)

• Question 1

Find the length of the line segment whose endpoints are at:

(4, 0) and (2, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
4.47
EDDIE SAYS
The x-part of the right-angled triangle is 4 - 2 = 2
The y-part of the right-angled triangle is 0 - 4 = -4 or 4
Pythagoras' Equation is d² = 2² + 4² = 20
• Question 2

Find the length of the line segment whose endpoints are at:

(4, 0) and (1, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
5
EDDIE SAYS
The x-part of the right-angled triangle is 4 - 1 = 3
The y-part of the right-angled triangle is 0 - 4 = -4 or 4
Pythagoras' Equation is d² = 3² + 4² = 25 (a 3,4,5 triad)
• Question 3

Find the length of the line segment whose endpoints are at:

(4, 3) and (7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
3.16
EDDIE SAYS
The x-part of the right-angled triangle is 4 - 7 = -3 or 3
The y-part of the right-angled triangle is 3 - 4 = -1 or 1
Pythagoras' Equation is d² = 3² + 1² = 10
• Question 4

Find the length of the line segment whose endpoints are at:

(4, -3) and (7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
7.62
EDDIE SAYS
The x-part of the right-angled triangle is 4 - 7 = -3 or 3
The y-part of the right-angled triangle is -3 - 4 = -7 or 7
Pythagoras' Equation is d² = 3² + 7² = 58
• Question 5

Find the length of the line segment whose endpoints are at:

(-4, 0) and (-7, 4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
5
EDDIE SAYS
The x-part of the right-angled triangle is -4 - -7 = 3
The y-part of the right-angled triangle is 0 - 4 = -4 or 4
Pythagoras' Equation is d² = 3² + 4² = 25 (3,4,5 triad)
• Question 6

Find the length of the line segment whose endpoints are at:

(14, -3) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
7.07
EDDIE SAYS
The x-part of the right-angled triangle is 14 - 7 = 7
The y-part of the right-angled triangle is -3 - -4 = 1
Pythagoras' Equation is d² = 7² + 1² = 50
• Question 7

Find the length of the line segment whose endpoints are at:

(4, -3) and (-4, 3)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
10
EDDIE SAYS
The x-part of the right-angled triangle is 4 - -4 = 8
The y-part of the right-angled triangle is -3 - 3 = -6 or 6
Pythagoras' Equation is d² = 8² + 6² = 100 (double a 3,4,5 triad)
• Question 8

Find the length of the line segment whose endpoints are at:

(14, 20) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
25
EDDIE SAYS
The x-part of the right-angled triangle is 14 - 7 = 7
The y-part of the right-angled triangle is 20 - -4 = 24
Pythagoras' Equation is d² = 7² + 24² = 625 (7,24,25 triad)
• Question 9

Find the length of the line segment whose endpoints are at:

(14, -20) and (7, -4)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
17.5
EDDIE SAYS
The x-part of the right-angled triangle is 14 - 7 = 7
The y-part of the right-angled triangle is -20 - -4 = -16 or 16
Pythagoras' Equation is d² = 7² + 16² = 305
• Question 10

Find the length of the line segment whose endpoints are at:

(12, 26) and (3, -14)

(Give your answer to 3 sig. figs. if it is not an integer)

CORRECT ANSWER
41
EDDIE SAYS
The x-part of the right-angled triangle is 12 - 3 = 9
The y-part of the right-angled triangle is 26 - -14 = 40
Pythagoras' Equation is d² = 9² + 24² = 625 (9,40,41 triad)
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