SPM 2018 Add Maths Paper 1, Question 23Coordinate Geometry

Solved on video in English and Bahasa Melayu · 4 marks · Form 4, Coordinate Geometry · 3:54 video

The question

Diagram 10 shows the position of three campsites A, B and C at a part of a riverbank drawn on a Cartesian plane, such that A and B lie on the same straight riverbank. Shah wants to cross the river from campsite C to the opposite riverbank where the campsites A and B are located. Find the shortest distance, in m, that he can take to cross the river. Give your answer correct to four decimal places.

[4 marks]

SPM 2018 Add Maths Paper 1, Question 23: the question as drawn in Eduly's video3:54

Step 1

The riverbank where A and B lie is the straight line AB. The shortest way for Shah to cross from C is the perpendicular (shortest) distance from C(4, -3) to line AB, call it CD.

Why this step

The shortest path from a point to a line is the perpendicular one. Don't measure CA or CB: those slanted lines are longer.

5 more steps, each with the reason for it, in the full solution

Final answer

66/√85 = 7.1587 m

Where students lose marks

Watch out: use the perpendicular distance from C to line AB, not CA or CB, and round only at the last step.

Watch every step of this question solved on video (3:54), with the reason behind each step and a box that checks your own answer.

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