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New
New
Year 10
Higher

Calculating the length of a line segment

I can calculate the length of a line segment on a coordinate grid in all four quadrants or using the coordinate pairs.

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New
New
Year 10
Higher

Calculating the length of a line segment

I can calculate the length of a line segment on a coordinate grid in all four quadrants or using the coordinate pairs.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Any line segment can be turned into a right-angled triangle by adding two lines which meet at 90°
  2. Calculating the horizontal distance gives the length of one side
  3. Calculating the vertical distance gives the length of the other side
  4. These two shorter sides lengths can be used to calculate the length of the line segment
  5. This can be done using Pythagoras' theorem

Common misconception

Pupils may think that direction matters when determining the distance between two points.

Direction matters when dealing with displacement, not distance.

Keywords

  • Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

  • Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Consider using a map and asking pupils to find the shortest (straight-line) distance between two points on the map. You could use a map of your local area. Are the distances the same as what the pupils expected? Is anywhere 'closer' than pupils thought it should be?
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
The coordinates (3, 8) translate to (7, 8). What is the change to the $$x$$-coordinate?
Correct Answer: 4, +4, increase by 4
Q2.
The coordinates (3, -8) translate to (7, 8). What is the change to the $$y$$-coordinate?
Correct Answer: 16, increase by 16, +16
Q3.
Work out the length of the hypotenuse, for this right-angled triangle.
An image in a quiz
Correct Answer: 101 cm, 101
Q4.
Work out the length of the edge marked $$x$$, for this right-angled triangle.
An image in a quiz
Correct Answer: 42 cm, forty two, 42
Q5.
M is the midpoint of a line segment AB. Given that A(4, 8) and B(6, 20), what are the coordinates of the midpoint M?
M(4, 14)
M(5, 10)
Correct answer: M(5, 14)
M(6, 12)
M(1, 6)
Q6.
M is the midpoint of a line segment AB. Given that A(5, 9) and M(8, 5), what are the coordinates of B?
B(6.5, 7)
B(3, -4)
B(2, 13)
Correct answer: B(11, 1)
B(1, 11)

Exit quiz

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6 Questions

Q1.
Put the length of these line segments in order, starting with the shortest.
An image in a quiz
1 - c
2 - a
3 - b
Q2.
What is the length of the line segment AB, to 1 decimal place?
An image in a quiz
Correct Answer: 7.6 units, 7.6
Q3.
What is the length of the line segment AB, to 1 decimal place?
An image in a quiz
Correct Answer: 5.8 units, 5.8
Q4.
Given that A(4, 7) and B(7, 11), what is the length of the line segment AB?
Correct Answer: 5 units, 5, five
Q5.
Given that A(-9, -9) and B(3, -4), what is the length of the line segment AB?
Correct Answer: 13 units, 13, thirteen
Q6.
Find the length of line segment CD starting at the origin with midpoint (4, 2). Give your answer to 2 decimal places.
Correct Answer: 8.94 units, 8.94