IB Maths AI HL AI 3.2 practice question

Question 1

Paper 1Hard6 marks

A flat map uses Cartesian coordinates to locate radio beacons. The segment $AB$ lies on the line $3x-4y-10=0$ and its midpoint is $M(2,-1)$

(a)

Determine the equation of the perpendicular bisector of $AB$ giving your answer in the form $ax+by+c=0$

[2]

(b)

Beacons $C$ and $D$ have coordinates $C(-2,4)$ and $D(4,2)$ An emergency receiver $Q$ must be equidistant from $A$ and $B$ and also equidistant from $C$ and $D$

Using your answer to (a), determine the exact coordinates of $Q$

[4]

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