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4MA1/1H Jan 2020, Question 1: Length of a Line Segment

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Given points A(5, −4) and B(13, 1) and line L with equation y = 2 − 3x, find the midpoint of AB, state the slope of L, and decide whether (100, −302) is on L with justification.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Calculate the coordinates of the point halfway between A(5, −4) and B(13, 1).

  1. 1Midpoint = (average of x, average of y)
  2. 2x: (5 + 13) ÷ 2 = 9
  3. 3y: (−4 + 1) ÷ 2 = −1.5
  4. 4Midpoint = (9, −1.5)

Answer(9, −1.5)

Part (b) · 1 mark

State the gradient of the line y = 2 − 3x.

  1. 1Gradient is the coefficient of x in y = 2 − 3x
  2. 2−3

Answer−3

Part (c) · 1 mark

Determine whether (100, −302) satisfies y = 2 − 3x, giving a reason.

  1. 1Substitute x = 100 into y = 2 − 3x
  2. 2y = 2 − 3(100) = 2 − 300 = −298
  3. 3The point (100, −302) does not lie on the line because −302 ≠ −298

AnswerNo, because when x = 100, y = 2 − 300 = −298, not −302

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