Exercises for Question Type 6: Identifying whether two lines are parallel or perpendicular

Exercises for Question Type 6: Identifying whether two lines are parallel or perpendicular - IB

Written by official IB examiners

Question 1

Skill question

Find the value of $k$ such that the lines $3 x - y + 2 = 0$ and $k x + 2 y - 5 = 0$ are perpendicular.

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Question 2

Skill question

Determine whether the line through points $(1, 2)$ and $(3, 6)$ is parallel, perpendicular, or neither to the line $y = 2 x - 1$ .

[3]

Question 3

Skill question

Determine whether the lines $x + y = 7$ and $x - y + 2 = 0$ are parallel, perpendicular, or neither.

[4]

Question 4

Skill question

Determine the relationship between the lines $y - 2 = 4 (x + 1)$ and $8 x + 2 y - 3 = 0$ .

[4]

Question 5

Skill question

Determine whether the lines $y = - 2 x + 5$ and $y = \frac{1}{2} x - 3$ are parallel, perpendicular, or neither.

[3]

Question 6

Skill question

Find the value of $b$ such that the lines $x + b y = 4$ and $2 x - y + 1 = 0$ are perpendicular.

[4]

Question 7

Skill question

Determine whether the lines $5 y - 10 x + 4 = 0$ and $2 x + y - 7 = 0$ are parallel, perpendicular, or neither.

[4]

Question 8

Skill question

For what value of $k$ is the line $y = k x + 3$ perpendicular to the line $4 x + 2 y - 6 = 0$ ?

[4]

Question 9

Skill question

Determine whether the lines $2 x - 4 y + 6 = 0$ and $x - 2 y - 3 = 0$ are parallel, perpendicular, or neither.

[4]

Question 10

Skill question

Determine whether the lines $y = 3 x + 1$ and $y = 3 x - 4$ are parallel, perpendicular, or neither.

[2]

Question 11

Skill question

Find the value of $k$ such that the lines $2 x + 5 y - 1 = 0$ and $k x - 10 y + 4 = 0$ are parallel.

[6]

Question 12

Skill question

Determine whether the lines $y = \frac{x + 2}{3}$ and $3 y - x - 6 = 0$ are parallel, perpendicular, or neither.

[4]

IB Mathematics Applications & Interpretation Question Type 6: Identifying Whether Two Lines Are Parallel or Perpendicular Exercises