IB Maths AI SL 3.5 Perpendicular bisectors Question Bank

Practise IB Mathematics SL/HL 3.5 by applying perpendicular bisectors methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[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 SL 3.5—Perpendicular bisectors 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)
(M1)
A1

Note: Award AO if parentheses are omitted in the final answer.

(b)

Find the equation of (XZ).

The equation of ( XY ) is y=2-x and the equation of (YZ) is y=0.5 x+3.5.

[ 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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SL 3.5—Perpendicular bisectors question 1

Question (a)

Question (b)