Which difference goes on top in the slope formula?

The change in y goes on top and the change in x goes on the bottom, taken in the same order for both points.

Can a distance between two points be negative?

No. Squares are never negative and the positive root is taken, so a distance is never negative.

Does the midpoint formula divide by 2?

Yes. A midpoint is the average position of the two points, so each coordinate is averaged by dividing by 2.

What are the slopes of a horizontal and a vertical line?

A horizontal line has slope 0, while a vertical line has no slope because the x-change is 0.

S4 Maths coordinate geometry paper 1: distance, midpoint and slope

2026-11-10

Tutor Prep Guide · S4 Maths Coordinate Geometry

Ten items start with distance and midpoint, then build slope, line equations and the parallel and perpendicular conditions.

Direct answers　Items 01 to 03 cover distance, midpoint and slope, 04 to 06 line equations, perpendicular slope and distance from the origin, 07 to 09 intercepts, a parallel test and a horizontal line, and 10 the reversed slope ratio.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S4 Maths Coordinate Geometry
Level	S4

02　Questions (10 items)

FoundationFind the distance between A(1, 2) and B(4, 6).
FoundationFind the coordinates of the midpoint of (2, -3) and (6, 5).
FoundationFind the slope of the line through (1, 2) and (5, 10).
IntermediateA line has slope 3 and passes through (2, 1). Find its equation.
IntermediateWhat is the slope of a line perpendicular to a line of slope 2/3?
IntermediateFind the distance from (3, 4) to the origin.
ChallengeFind the y-intercept of the line 2x + 3y = 12.
ChallengeAre the lines y = 2x + 1 and y = 2x – 5 parallel? Explain.
ChallengeFind the equation of the horizontal line through (5, -2).
Error redoFind the slope of the line through (1, 1) and (4, 7). A student answered 1/2.

03　Answers and one-line notes

#	Answer	One-line note
1	5	The horizontal change is 4 – 1 = 3 and the vertical change is 6 – 2 = 4, so the distance is the square root of 9 + 16, which is 5.
2	(4, 1)	The x-coordinate is (2 + 6) / 2 = 4 and the y-coordinate is (-3 + 5) / 2 = 1.
3	2	Slope is the change in y over the change in x, that is (10 – 2) / (5 – 1) = 8 / 4 = 2.
4	y = 3x – 5	Write y = 3x + c; substituting (2, 1) gives 1 = 6 + c, so c = -5.
5	-3/2	Perpendicular slopes multiply to -1, so the slope is -1 divided by 2/3, which is -3/2.
6	5	The origin is (0, 0), so the distance is the square root of 9 + 16, which is 5.
7	4	Putting x = 0 gives 3y = 12, so y = 4 and the intercept is (0, 4).
8	Parallel, because both have slope 2 while their intercepts differ.	Parallel lines need equal slopes: both have slope 2, and the constants 1 and -5 differ, so the lines are parallel.
9	y = -2	Every point on a horizontal line has the same y-coordinate, so through (5, -2) the equation is y = -2.
10	2; the answer 1/2 comes from dividing the x-change by the y-change.	The slope is (7 – 1) / (4 – 1) = 6 / 3 = 2; dividing the x-change by the y-change wrongly gives 1/2.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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