CAIE A-Level Mathematics 1.3.2 Straight-Line Equation Forms

Practise finding gradients, midpoints and perpendicular bisectors and expressing straight lines in gradient-intercept, point-gradient or general linear form.

Exam points

calculate a midpoint and use the negative reciprocal gradient for a perpendicular bisector
form y − y₁ = m(x − x₁) from a point and gradient before rearranging as required
verify parallel or perpendicular lines using equal gradients or a gradient product of −1

[Maximum number: 2]

Points A(-2,3), B(3,0) and C(6,5) lie on the circumference of a circle with centre D.

Show that angle $A B C=90^{\circ}$ .

Gradient of $A B=-\frac{3}{5}$ , gradient of $B C=\frac{5}{3}$ or lengths of all 3 sides or vectors
M1
Attempting to find required gradients, sides or
vectors
$m_{a b} m_{b c}=-1$ or Pythagoras or $\overrightarrow{A B} \cdot \overrightarrow{B C}=0$ or $\cos A B C=0$ from cosine rule
A1
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1.3.2—Line equation forms question 1