This article covers the essential skills of coordinate geometry – a core topic in DSE Paper 1 Section A(1) and A(2) worth 3–5 marks. You will learn how to find the distance between two points using the distance formula, the midpoint of a line segment, and the slope of a straight line. You will also learn how to write the equation of a straight line in various forms and how to determine parallel and perpendicular relationships between lines. The article includes step-by-step worked examples, DSE exam techniques, practice questions. These are essential skills that appear regularly in DSE papers.
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Coordinate Geometry (Part 1) | Distance, Midpoint & Slope
Question 1 MC
Find the distance between \( (-1, 4) \) and \( (5, -4) \).
A. \( 8 \) B. \( 10 \) C. \( 12 \) D. \( 14 \)
Question 2 MC
What is the midpoint of \( (2, -3) \) and \( (8, 7) \)?
A. \( (4, 2) \) B. \( (5, 2) \) C. \( (3, 5) \) D. \( (10, 4) \)
Question 3 Short Answer
Find the slope of the line through \( (0, 0) \) and \( (-3, 6) \).
Question 4 Short Answer
Find the equation of the line with slope \( 2 \) passing through \( (-2, 1) \).
Question 5 MC
Which line is parallel to \( y = -2x + 3 \)?
A. \( y = -\frac{1}{2}x + 1 \) B. \( y = 2x - 4 \) C. \( y = -2x + 7 \) D. \( y = \frac{1}{2}x + 3 \)
Question 6 Short Answer
Find the midpoint of \( (-4, 5) \) and \( (6, -3) \).
Question 7 MC
The slope of a line is undefined. What type of line is it?
A. Horizontal B. Vertical C. Diagonal D. Curved
Question 8 Short Answer
Find the equation of the line through \( (1, 2) \) and \( (3, 8) \).
Question 9 Short Answer
Determine if the lines \( y = 4x - 1 \) and \( y = -\frac{1}{4}x + 2 \) are perpendicular.
Question 10 Short Answer
Find the distance between \( (-2, -3) \) and \( (4, 5) \).
When using the distance formula, remember to square the differences before adding. Also, the distance is always positive – take the positive square root. For slope, be careful with undefined slope (vertical lines) where \( x_2 = x_1 \).