Equations of lines in any form, parallel and perpendicular gradients, intersection of two lines, midpoints, perpendicular bisectors and simple problems.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Two points define a line. From them you can write its equation, find its perpendicular, locate where it meets another line — all with a few lines of algebra.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the gradient and intercept; add a parallel or perpendicular line.
Copy these into your notebook in your own words — that is how they stick.
m = (y₂ − y₁)/(x₂ − x₁); from ax + by + c = 0, m = −a/b.
y − y₁ = m(x − x₁); or y = mx + c; or ax + by + c = 0.
m₁ = m₂.
m₁m₂ = −1.
Solve the two equations simultaneously.
((x₁ + x₂)/2, (y₁ + y₂)/2).
Through the midpoint with the negative reciprocal gradient.
Equal gradients between successive pairs of points.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (25 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [13 marks]
The vertices of a triangle are A(1, 1), B(7, 3) and C(2, −2).
(a) Find the gradient of AB and the equation of AC. [4]
(b) Show that angle BAC = 90°. [2]
(c) Find the equation of the line through A parallel to BC. [3]
(d) Calculate the area of triangle ABC. [4]
Question 2 [12 marks]
A(1, 2) and B(7, 10) are two points.
(a) Find the midpoint M of AB and the gradient of AB. [3]
(b) Show that the perpendicular bisector of AB has equation 3x + 4y = 36. [3]
(c) The perpendicular bisector meets the axes at P and Q. Find the area of triangle OPQ, where O is the origin. [4]
(d) Show that C(10, 14) lies on the line AB. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.