SL 3.5—Intersection of lines, equations of perpendicular bisectors - IB Questionbank | RevisionDojo

SL 3.5—Intersection of lines, equations of perpendicular bisectors Questionbank

Practice SL 3.5—Intersection of lines, equations of perpendicular bisectors with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

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 $Q$ .

Calculate the ratio $P A: A Q$ .

[7]

Question 3

SLPaper 1

Given that the points $A(2,1), B(t, 2 t)$ , and $C\left(t^{2}, 5 t-3\right)$ are collinear, find all possible values of $t$ .

[7]

Question 4

SLPaper 1

The equations of the sides $A B, B C$ , and $C A$ of triangle $A B C$ are given as:

A B: y=-x, \quad B C: y=2 x, \quad C A: x+y=6

Find the coordinates of point $C$ . Then, determine the equation of the line through $C$ that is perpendicular to line $A B$ . This line intersects the $x$ -axis at point $P$ and the $y$ -axis at point $Q$ . Calculate the ratio $P C C Q$ .

[7]

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]

Question 6

SLPaper 1

Find the gradient of the line that passes through the points $\mathrm{A}(2,3)$ and $\mathrm{B}(6$ , 7).

[2]

Question 7

SLPaper 1

A line passes through the point $\mathrm{P}(2,-1)$ and has a gradient of 3 .

Find the equation of the line in the form $y=m x+c$ .

[3]

Question 8

SLPaper 2

Calculate the perpendicular distance from the point $P(2,5)$ to the line joining the points $A(1,-2)$ and $B(5,4)$ .

[5]

Question 9

SLPaper 1

Determine the coordinates of the midpoint of the segment joining $\mathrm{A}(4,2)$ and $\mathrm{B}(10,8)$ .

[2]

Question 10

SLPaper 1

Let the points be $A(t, t+1)$ and $B(3 t, 3)$ .

Show that the equation of the perpendicular bisector of segment $A B$ is

y+t x=2 t^{2}+t+2

[4]

Given that this perpendicular bisector passes through the point (5, 2), find the value of $t$ .

[2]

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 $Q$ .

Calculate the ratio $P A: A Q$ .

[7]

Question 3

SLPaper 1

Given that the points $A(2,1), B(t, 2 t)$ , and $C\left(t^{2}, 5 t-3\right)$ are collinear, find all possible values of $t$ .

[7]

Question 4

SLPaper 1

The equations of the sides $A B, B C$ , and $C A$ of triangle $A B C$ are given as:

A B: y=-x, \quad B C: y=2 x, \quad C A: x+y=6

[7]

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]

Question 6

SLPaper 1

Find the gradient of the line that passes through the points $\mathrm{A}(2,3)$ and $\mathrm{B}(6$ , 7).

[2]

Question 7

SLPaper 1

A line passes through the point $\mathrm{P}(2,-1)$ and has a gradient of 3 .

Find the equation of the line in the form $y=m x+c$ .

[3]

Question 8

SLPaper 2

Calculate the perpendicular distance from the point $P(2,5)$ to the line joining the points $A(1,-2)$ and $B(5,4)$ .

[5]

Question 9

SLPaper 1

Determine the coordinates of the midpoint of the segment joining $\mathrm{A}(4,2)$ and $\mathrm{B}(10,8)$ .

[2]

Question 10

SLPaper 1

Let the points be $A(t, t+1)$ and $B(3 t, 3)$ .

Show that the equation of the perpendicular bisector of segment $A B$ is

y+t x=2 t^{2}+t+2

[4]

Given that this perpendicular bisector passes through the point (5, 2), find the value of $t$ .

[2]