Parallel and Perpendicular Lines
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Parallel and Perpendicular Lines — Free MYP4 Mathematics (Standard) 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

2QuestionVerifying Line Relationships AlgebraicallyAssessment Practice
4 marks~6 minCriterion D
A landscape designer is planning a sprinkler system for a rectangular garden. A main water pipe runs along the line

y=2x+1y = 2x + 1

where units are in metres. A perpendicular sprinkler line must pass through the point (3,5)(3, 5), where a new flower bed is located.
a
Deduce the equation of the sprinkler line in slope-intercept form. [2]
b
The designer assumes the main pipe has an exact slope of 22. Advise the designer whether this linear model is sufficient for final installation of the sprinkler line, given that the measured slope of the main pipe may vary within 2±0.12 \pm 0.1 and that physical obstacles may exist. [2]
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Solutions

3QuestionGradient of Perpendicular LinesConcept Practice
2 marks~3 minCriterion C
An urban planner is designing a city block. Two roads must be built so that they intersect at exactly 90°.

Road A follows the line y=3x−5y = 3x - 5.

Road B passes through the point (6,1)(6, 1) and must be perpendicular to Road A.
a
State the gradient of Road B. [1]
b
The planner claims Road B can be represented by y=−13x+3y = -\dfrac{1}{3}x + 3. Justify whether this equation is correct and whether the road design meets the 90° requirement. [1]

Solutions

4QuestionUsing Slope Relationships in GraphsAssessment Practice
4 marks~6 minCriterion B
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

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