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Lesson 9 of 11

    Ratios in line segments on coordinate axes

    I can use ratios to divide a line segment and find the coordinates of a point on the line.

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    Lesson 9 of 11
    New
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      Ratios in line segments on coordinate axes

      I can use ratios to divide a line segment and find the coordinates of a point on the line.

      Download all

      Lesson details

      Key learning points

      1. Your knowledge of ratios can be applied here.
      2. The ratio can be applied to both the x and y distances.
      3. Your knowledge of similar triangles explains why this works for diagonal lines.

      Keywords

      • Midpoint - The midpoint of a line segment is halfway between the two end points.

      Common misconception

      P is a point such that AP : PB is in the ratio of 1 : 3 means that point P is a third of the distance of AB from A.

      There are 4 equal parts in total, meaning that point P is a quarter of the distance of AB from A.

      Calculating the midpoint is shown via the ratio method so that pupils can then build on this understanding for when the line is split into different ratios. This is in preparation for vectors which are introduced in Year 11.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Which of the below are ratios?

      Correct answer: $$2:3$$
      Correct answer: $$1:2.5$$
      $$2.5$$
      $$2\over5$$
      Correct answer: $${1\over2}:{2\over5}$$

      Q2.
      Match each ratio to an equivalent ratio.

      Correct Answer:1 : 2,12 : 24

      12 : 24

      Correct Answer:2 : 1,12 : 6

      12 : 6

      Correct Answer:1 : 3,8 : 24

      8 : 24

      Correct Answer:2 : 3,12 : 18

      12 : 18

      Correct Answer:3 : 2,18 : 12

      18 : 12

      Q3.
      Two Oak pupils share 30 sweets in the ratio of 1 : 1. What proportion of the sweets does the second pupil receive?

      One whole
      $$1\over1$$
      Correct answer: $$1\over2$$
      $$1\over3$$

      Q4.
      £280 is divided in the ratio of 1 : 4. Which calculation can be used to find the larger share?

      $$280\div5$$
      Correct answer: $$(280\div5)\times4$$
      $${1\over5}\times280$$
      Correct answer: $${4\over5}\times280$$
      $$(280\div4)\times1$$

      Q5.
      8640 grams is divided in the ratio of 3 : 5. How much is in the smaller share?

      1080 g
      1728 g
      Correct answer: 3240 g
      5400 g
      5184 g

      Q6.
      What number is exactly in the middle of -17 and 60?

      21
      Correct answer: 21.5
      23
      23.5
      38.5

      Assessment exit quiz

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      6 Questions

      Q1.
      Halfway between the two end points of a line segment is the ...

      half point
      median
      Correct answer: midpoint

      Q2.
      Three points A, B and P are plotted. If AP : PB is in the ratio of 1 : 1 then P is the of AB.

      Correct Answer: midpoint, mid point, mid-point

      Q3.
      What is the midpoint of line segment AB?

      An image in a quiz
      (7, 3)
      Correct answer: (8, 5)
      (8.5, 6)
      (9, 7)

      Q4.
      Find the coordinates of the point P when AP : PB is in the ratio 3 : 1.

      An image in a quiz
      (7, 3)
      (8, 5)
      (8.5, 6)
      Correct answer: (9, 7)

      Q5.
      Find the coordinates of the point P when AP : PB is in the ratio 1 : 4.

      An image in a quiz
      Correct answer: (-3, 0)
      (-1, -1)
      (0, -1.5)
      (1, -2)
      (3, -3)

      Q6.
      Find the coordinates of the point P when AP : PB is in the ratio 3 : 2.

      An image in a quiz
      (-3, 0)
      (-1, -1)
      (0, -1.5)
      Correct answer: (1, -2)
      (3, -3)

      Lesson appears in

      UnitMaths / Linear graphs

      Maths

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