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Midpoint of a line segment practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of midpoint of a line segment questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Work out the coordinates of the midpoint of (2, 4) and (6, 10).

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Answer: (4, 7)

  1. x-midpoint: (2 + 6)/2 = 4.
  2. y-midpoint: (4 + 10)/2 = 7.
  • Method (1): x-midpoint: (2 + 6)/2 = 4.
  • Accuracy (1): y-midpoint: (4 + 10)/2 = 7.

Question 2 Easy

Work out the coordinates of the midpoint of (0, 2) and (8, 4).

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Answer: (4, 3)

  1. x-midpoint: (0 + 8)/2 = 4.
  2. y-midpoint: (2 + 4)/2 = 3.
  • Method (1): x-midpoint: (0 + 8)/2 = 4.
  • Accuracy (1): y-midpoint: (2 + 4)/2 = 3.

Question 3 Medium

Work out the y-coordinate of the midpoint of (1, 8) and (5, 2).

Show answer

Answer: 5

  1. Identify y-values 8 and 2.
  2. Average: (8 + 2)/2 = 5.
  • Method (1): Identify y-values 8 and 2.
  • Accuracy (1): Average: (8 + 2)/2 = 5.

Question 4 Medium

Work out the y-coordinate of the midpoint of (2, 4) and (6, 10).

Show answer

Answer: 7

  1. Identify y-values 4 and 10.
  2. Average: (4 + 10)/2 = 7.
  • Method (1): Identify y-values 4 and 10.
  • Accuracy (1): Average: (4 + 10)/2 = 7.

Question 5 Hard

Work out the distance between (2, 1) and (5, 5).

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Answer: 5

  1. dx = 3, dy = 4.
  2. Distance = √(9 + 16) = √25 = 5.
  • Method (1): dx = 3, dy = 4.
  • Accuracy (1): Distance = √(9 + 16) = √25 = 5.

Question 6 Hard

Work out the distance between (1, 1) and (4, 5).

Show answer

Answer: 5

  1. dx = 3, dy = 4.
  2. Distance = √(9 + 16) = 5.
  • Method (1): dx = 3, dy = 4.
  • Accuracy (1): Distance = √(9 + 16) = 5.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Work out the coordinates of the midpoint of (4, 2) and (8, 10).

Show answer

Answer: (6, 6)

  1. Sum coordinates: (4+8) = 12 and (2+10) = 12.
  2. Halve each sum: 12/2 = 6 and 12/2 = 6, giving (6, 6).
  • Method (1): (4 + 8)/2 or (2 + 10)/2
  • Accuracy (1): (6, 6)

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

How do you find the midpoint of two points (x_A, y_A) and (x_B, y_B)?

  1. ((x_A+x_B)/2, (y_A+y_B)/2)
  2. ((x_B-x_A)/2, (y_B-y_A)/2)
  3. (x_A+x_B, y_A+y_B)
Show answer

((x_A+x_B)/2, (y_A+y_B)/2) Average the x-coordinates and average the y-coordinates.

Check 2

What is the midpoint of (2, 6) and (8, 2)?

  1. (5, 4)
  2. (10, 8)
  3. (6, 4)
Show answer

(5, 4) (2+8)/2 = 5 and (6+2)/2 = 4.

Check 3

What is the midpoint of (0, 0) and (4, 6)?

  1. (2, 3)
  2. (4, 6)
  3. (2, 6)
Show answer

(2, 3) (0+4)/2 = 2 and (0+6)/2 = 3.

Check 4

What is the midpoint of (1, 2) and (5, 8)?

  1. (3, 5)
  2. (6, 10)
  3. (4, 5)
Show answer

(3, 5) (1+5)/2 = 3 and (2+8)/2 = 5.

Check 5

What is the x-coordinate of the midpoint of (1, 8) and (7, 2)?

  1. 4
  2. 5
  3. 8
Show answer

4 (1+7)/2 = 4.

Check 6

What is the y-coordinate of the midpoint of (1, 8) and (5, 2)?

  1. 5
  2. 3
  3. 6
Show answer

5 (8+2)/2 = 5.

Check 7

What is the x-coordinate of the midpoint of (0, 3) and (6, 1)?

  1. 3
  2. 2
  3. 6
Show answer

3 (0+6)/2 = 3.

Check 8

What is the y-coordinate of the midpoint of (2, 4) and (6, 10)?

  1. 7
  2. 4
  3. 8
Show answer

7 (4+10)/2 = 7.

Check 9

How do you calculate the distance between two points on a coordinate grid?

  1. Use Pythagoras: √((dx)^2 + (dy)^2)
  2. Add dx and dy
  3. Multiply dx by dy
Show answer

Use Pythagoras: √((dx)^2 + (dy)^2) The horizontal and vertical differences form legs of a right triangle.

Check 10

What is the distance between (0, 0) and (6, 8)?

  1. 10
  2. 14
  3. 48
Show answer

10 √(36 + 64) = √100 = 10.

Check 11

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

  1. 13
  2. 17
  3. 60
Show answer

13 √(25 + 144) = √169 = 13.

Check 12

What is the distance between (1, 2) and (4, 6)?

  1. 5
  2. 7
  3. 12
Show answer

5 dx = 3, dy = 4, so √(9 + 16) = 5.

Check 13

Why must you divide by 2 when finding a midpoint?

  1. The midpoint is the mean (halfway)
  2. To change to scale factor
  3. Because there are two axes
Show answer

The midpoint is the mean (halfway) The midpoint is equidistant from both endpoints, which is their arithmetic mean.

Check 14

Can you average an x-coordinate with a y-coordinate?

  1. No, keep axes separate
  2. Yes, always
  3. Only if they are equal
Show answer

No, keep axes separate x and y represent perpendicular, independent directions.

Check 15

What is the distance between (2, 1) and (5, 5)?

  1. 5
  2. 7
  3. 6
Show answer

5 dx = 3, dy = 4, so distance is 5.

Keep going with Midpoint of a line segment

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