4MA1/2F January 2022 Question 5: Length of a Line Segment

Question 1

On the grid, draw the horizontal line y = −2.

Accepted Answer

Every point on the line y = −2 has y-coordinate −2 Find −2 on the y-axis Draw a horizontal straight line through that point, from x = −5 across to x = 7 Answer: A horizontal straight line right across the grid through (−5, −2) and (7, −2)

Question 2

Calculate the coordinates of M, the midpoint of AB.

Accepted Answer

From the grid, A = (−3, 1) and B = (1, 3) x-coordinate of M = (−3 + 1) ÷ 2 = −1 y-coordinate of M = (1 + 3) ÷ 2 = 2 M = (−1, 2) Answer: (−1, 2)

Question 3

Given D is (5, d) with d > 0 and triangle ABD is isosceles, find d.

Accepted Answer

From the grid, A = (−3, 1) and B = (1, 3) From A to B is 4 right and 2 up, so AB = √(4² + 2²) = √20 D = (5, d) is 4 right of B, so going 2 down from B gives D = (5, 1) and BD = √(4² + 2²) = √20 BD = AB, so triangle ABD is isosceles Going 2 up from B instead gives (5, 5), which lies on the straight line through A and B, so that gives no triangle d = 1 Answer: 1

4MA1/2F Jan 2022, Question 5: Length of a Line Segment

The question, in short

Part (a) · 1 mark

Part (b) · 2 marks

Part (c) · 1 mark

Practise more length of a line segment questions

More past-paper questions on length of a line segment