Parallel and Perpendicular Lines
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 51 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Parallel and Perpendicular Lines — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionGradient of Parallel LinesConcept Practice
2 marks~3 minCriterion A
A city planner is designing two parallel cycle lanes on a coordinate grid, where each unit represents 50 metres. Lane A passes through the points (0,1)(0, 1) and (3,3)(3, 3).

(a) Deduce the gradient of Lane B. [2]
Question diagram

Solutions

2QuestionGradient of Perpendicular LinesAssessment Practice
2 marks~3 minCriterion D
A city engineer is designing two straight roads that must intersect at a right angle. Road L1L_1 has a gradient of 22.
a
Deduce the gradient of road L2L_2, given that L1⊥L2L_1 \perp L_2. [1]
b
The engineer states: "A road with a gradient steeper than −1-1 is unsafe for heavy vehicles." Advise the engineer whether road L2L_2 is suitable for heavy vehicles, justifying your answer with an inequality comparison. [1]
Question diagram

Solutions

3QuestionUsing Slope Relationships in GraphsAssessment Practice
4 marks~6 minCriterion C
A city architect is designing two straight pedestrian pathways that must meet at a perfect right angle to ensure safe sightlines at an intersection.

The architect models the pathways on a coordinate grid.

Pathway A: y=34x−2y = \dfrac{3}{4}x - 2

Pathway B: y=−43x+5y = -\dfrac{4}{3}x + 5
a
Calculate the slope of each pathway. [1]
b
Deduce, using your results from part (a), the general rule relating the slopes of any two perpendicular lines. [1]
c
The architect proposes a third pathway, y=25x+1y = \dfrac{2}{5}x + 1, to intersect Pathway A at a right angle. Advise the architect whether this proposed pathway satisfies the perpendicularity condition, and state the correction required if it does not. [2]

Solutions

4QuestionVerifying Line Relationships AlgebraicallyAssessment Practice
6 marks~9 minCriterion B
An urban planner is designing a city block. Two roads are being built: Road A has slope m1=34m_1 = \dfrac{3}{4} and Road B has slope m2=−43m_2 = -\dfrac{4}{3}. A third road, Road C, runs parallel to Road A with slope m3=34m_3 = \dfrac{3}{4}.
a
Calculate m1×m2m_1 \times m_2 and m1×m3m_1 \times m_3. [2]
b
Deduce the general algebraic relationship between the slopes of two perpendicular lines and between the slopes of two parallel lines. [2]
c
The planner claims Roads A and B form a perfect right-angle intersection, required by the city's safety code. Justify whether this claim is correct, and advise the planner on what adjustment to Road B's slope would be needed if it were instead built with slope m=−54m = -\dfrac{5}{4}. [2]

Solutions

Questions 5-55

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 55.

+51 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade