IB Maths AI SL 3.5 Perpendicular Bisectors Questions

Practise finding midpoints and gradients, constructing perpendicular bisectors, and checking equal-distance or perpendicularity conditions in the resulting region.

Exam points

Find the midpoint and gradient of a segment and construct the perpendicular bisector equation.
Use two points or a segment equation plus midpoint to determine a perpendicular-bisector boundary.
Check the line by equal-distance or perpendicularity reasoning and interpret the resulting region.

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Study SL 3.5—Perpendicular bisectors conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

The Voronoi diagram below shows four supermarkets represented by points with coordinates A(0,0), B(6,0), C(0,6) and D(2,2). The vertices X, Y, Z are also shown. All distances are measured in kilometres.

Figure for Question IB Maths AI SL 3.5 Perpendicular Bisectors Questions question 1 — IB Maths AI SL

(a)

Find the midpoint of $[\mathrm{BD}]$ .

[ 2 ]

$\left(\frac{2+6}{2}, \frac{2+0}{2}\right)$
(4,1)
Note: Award AO if parentheses are omitted in the final answer.

(b)

Find the equation of (XZ).

[ 4 ]

attempt to substitute values into gradient formula
$\left(\frac{0-2}{6-2}=\right)-\frac{1}{2}$
therefore the gradient of perpendicular bisector is 2

\text { so } y-1=2(x-4) \quad(y=2 x-7)

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IB Maths AI SL 3.5 Perpendicular Bisectors Questions question 1

Question (a)

Question (b)