IB Mathematics Applications & Interpretation Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

The line joining the points $A (2, - 4)$ and $B (6, 8)$ meets the $x$ - and $y$ -axes at the points $P$ and $Q$ , respectively.

Find the equation of line $A B$ and calculate the length of the segment $P Q$ .

[5]

Question 2

SLPaper 1

The line through the point $A (2, - 3)$ is perpendicular to the line $2 x + y = 5$ . This new line intersects the $x$ -axis at point $P$ and the $y$ -axis at point $Q$ .

Find the equation of the line through $A$ and determine the coordinates of $P$ and $Q$ .

[4]

Calculate the ratio $P A : A Q$ .

[3]

Question 3

SLPaper 1

On a coordinate map, two emergency beacons are at $P (- 5, 4)$ and $Q (1, - 2)$ . The boundary separating their signal zones is the set of all points equidistant from $P$ and $Q$ .

Determine the equation of this boundary, expressing your answer in the form $y = m x + c$ .

[3]

Question 4

SLPaper 2

The triangle

A B C

has vertices

A (- 2, 0)

B (4, 0)

, and

C (2, 6)

Find the equation of the perpendicular bisector of $[A B]$ .

[2]

Find the equation of the perpendicular bisector of $[A C]$ , giving your answer in the form $y = m x + c$ .

[4]

Find the coordinates of $P$ , the point of intersection of the two perpendicular bisectors.

[2]

Find the radius of the circle that passes through $A$ , $B$ , and $C$ .

[3]

Hence write down the equation of the circle passing through $A$ , $B$ , and $C$ .

[2]

Question 5

SLPaper 1

The straight line passing through the points $(1, 4)$ and $(7, - 2)$ intersects the line $x + 2 y = 10$ at the point $P$ .

Find the coordinates of $P$ .

[5]

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

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IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

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