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Find the Midpoint

In this worksheet, students will find the coordinates of a midpoint of a line segment.

'Find the Midpoint' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra, Graphs of Equations and Functions

Curriculum subtopic:   Graphs, Straight Line Graphs

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

To find the middle between two numbers, we can add them together and then divide by 2.

For example, the middle between 4 and 7 is 4 + 7 = 11, 11 ÷ 2 = 5.5.

You can use the same method to find the midpoint (the middle) of a line segment.

A line segment is simply a part of a line between two points. A line segment has a beginning and the end.

 

Let's say we have a line segment between (1, 2) and (5, 6).

We need to find the middle between the x-coordinates and the y-coordinates.

Simply add the x-coordinates and divide by 2, then add the y-coordinates and divide by 2.

 

1 + 5 = 6

6 ÷ 2 = 3

2 + 6 = 8

8 ÷ 2 = 4

 

The coordinates of the midpoint of this line segment are (3, 4).

 

Find the midpoint between (1, 8) and (9, 2).

(10, 10)

(1.5 , 8.3)

(5, 5)

(6, 7)

Find the midpoint between (1, 8) and (9, 2).

(10, 10)

(1.5 , 8.3)

(5, 5)

(6, 7)

Find the midpoint of a line segment between (0, -3) and (7, -1).

(3.5, -1)

(7, -4)

(3.5, -2)

(3.5, 2)

Match the pairs of points to their midpoints.

Column A

Column B

(-2, 5) and (4, -1)
(1, 3)
(-4, -2) and (2, 4)
(-1, 1)
(-2, 4) and (4, 2)
(1, 2)
(-7 -4) and (-2, -1)
(-4.5, -2,5)

Find the midpoint of (-7, -2) and (3, -5)

(-10, 3)

(-5, 1.5)

(-4, -7)

(-2, -3.5)

A line segment has a starting point (4, 5).

The midpoint is (6, 8).

What are the coordinates of the end point?

(5, 6.5)

(8, 11)

(6.5, 5)

(10, 13)

True or False?

If the start point of a line segment is (3, 11) and the midpoint is (7, 17), the end point must be (5, 14).

True

False

The midpoint of a line segment AB is (-3, 3).

Point A has coordinates (-6, 8).

What are the coordinates of point B?

(-6, 6)

(-4.5, 6.5)

(0, -2)

(-3, 3)

Find the coordinates of a midpoint of a line segment AB, where A and B have coordinates:

A = (2p, q)

B = (6p, 7q)

(10p, 13q)

(8p, 8q)

(4p, 4q)

(-2p, -5q)

Find the coordinates of a midpoint of a line segment AB, where A and B have coordinates:

A = (8p, 2q)

B = (2p, 14q)

(10p, 16q)

(14p, 26q)

(5p, 8q)

(-2p, -5q)

  • Question 1

Find the midpoint between (1, 8) and (9, 2).

CORRECT ANSWER
(5, 5)
EDDIE SAYS
Remember, add the corresponding coordinates and divide by 2. 1 + 9 = 10 10 ÷ 2 = 5 8 + 2 = 10 10 ÷ 2 = 5 Make sure you divide by 2. This is where students go wrong usually!
  • Question 2

Find the midpoint between (1, 8) and (9, 2).

CORRECT ANSWER
(5, 5)
EDDIE SAYS
Remember, add the corresponding coordinates and divide by 2. 1 + 9 = 10 10 ÷ 2 = 5 8 + 2 = 10 10 ÷ 2 = 5 Make sure you divide by 2. This is where students go wrong usually!
  • Question 3

Find the midpoint of a line segment between (0, -3) and (7, -1).

CORRECT ANSWER
(3.5, -2)
EDDIE SAYS
Follow the same method as we did before, but make sure that you're careful with those negative numbers! 0 + 7 = 7 7 ÷ 2 = 3.5 -3 + (-1) = -4 -4 ÷ 2 = -2 The midpoint is (3.5, -2).
  • Question 4

Match the pairs of points to their midpoints.

CORRECT ANSWER

Column A

Column B

(-2, 5) and (4, -1)
(1, 2)
(-4, -2) and (2, 4)
(-1, 1)
(-2, 4) and (4, 2)
(1, 3)
(-7 -4) and (-2, -1)
(-4.5, -2,5)
EDDIE SAYS
.
  • Question 5

Find the midpoint of (-7, -2) and (3, -5)

CORRECT ANSWER
(-2, -3.5)
EDDIE SAYS
There's quite a few negative numbers here, so be careful how you add them. -7 + 3 = -4 4 ÷ 2 = -2 -2 + -5 = -7 -7 ÷ 2 = -3.5 The midpoint is (-2, -3.5).
  • Question 6

A line segment has a starting point (4, 5).

The midpoint is (6, 8).

What are the coordinates of the end point?

CORRECT ANSWER
(8, 11)
EDDIE SAYS
Here you need to work backwards as you have one of the points and the midpoint. The midpoint is (6, 8). This means that after adding the coordinates you get (12, 16). (Because then we would divide by 2 to get (6, 8)). x-coordinates must add to 12. 12 - 4 = 8, so the end has x-coordinate 8. y-coordinates must add to 16. 16 - 5 = 11, so the end has y-coordinate 11. The coordinates of the endpoint are (8, 11)
  • Question 7

True or False?

If the start point of a line segment is (3, 11) and the midpoint is (7, 17), the end point must be (5, 14).

CORRECT ANSWER
False
EDDIE SAYS
This is false! If the start point is (3, 11) and the midpoint is (7, 17), then the coordinates of the start and the end points must add to (14, 34) (double the coordinates of the midpoint). 14 - 3 = 11 34 - 11 = 23 The coordinates of the end point are (11, 23).
  • Question 8

The midpoint of a line segment AB is (-3, 3).

Point A has coordinates (-6, 8).

What are the coordinates of point B?

CORRECT ANSWER
(0, -2)
EDDIE SAYS
The coordinates of the midpoint are (-3, 3) so the coordinates of A and B must add to double that, which is (-6, 6). -6 - (-6) = 6 + 6 = 0 The x-coordinate is 0. 6 - 8 = -3 The y-coordinate is -3. The coordinates of point B are (0, -3).
  • Question 9

Find the coordinates of a midpoint of a line segment AB, where A and B have coordinates:

A = (2p, q)

B = (6p, 7q)

CORRECT ANSWER
(4p, 4q)
EDDIE SAYS
Don't be put off by this question! The coordinates are given in an algebraic form, but the same method can be used to find the midpoint of this line segment. Add the corresponding coordinates and divide by 2. 2p + 6p = 8p 8p ÷ 2 = 4p q + 7q = 8q 8q ÷ 2 = 4q The coordinates of the midpoint are (4p, 4q).
  • Question 10

Find the coordinates of a midpoint of a line segment AB, where A and B have coordinates:

A = (8p, 2q)

B = (2p, 14q)

CORRECT ANSWER
(5p, 8q)
EDDIE SAYS
Here's another questions involving algebra. Have a look below to see the method to find the correct midpoint of the line segment AB. 8p + 2p = 10p 10p ÷ 2 = 5p 2q + 14q = 16q 16q ÷ 2 = 8q The coordinates of the midpoint are (5p, 8q).
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