Parallel and Perpendicular Lines
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Parallel and Perpendicular Lines — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionVerifying Line Relationships AlgebraicallyConcept Practice
2 marks~3 minCriterion A
A city planner is checking whether two proposed roads are perpendicular before approving a junction design. Road L1L_1 passes through points A(1,2)A(1, 2) and B(3,8)B(3, 8). Road L2L_2 passes through points C(4,1)C(4, 1) and D(7,2)D(7, 2).
a
Calculate the gradient of L1L_1 and the gradient of L2L_2. [1]
b
Advise the city planner whether the junction design should be approved on the basis of perpendicularity, justifying your answer using the gradients found in part (a). [1]
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Solutions

2QuestionVerifying Line Relationships AlgebraicallyAssessment Practice
6 marks~9 minCriterion D
A surveyor uses GPS coordinates to map two straight fence lines on a farm. The first fence line passes through A(2,1)A(2, 1) and B(8,5)B(8, 5). The second fence line passes through C(3,6)C(3, 6) and D(7,0)D(7, 0). The farmer claims the two fence lines are perpendicular and plans to install a gate that fits exactly in the corner between them.
a
Calculate the gradient of each fence line. [2]
b
Justify whether the two fence lines are perpendicular. [2]
c
The GPS has a systematic error of ±5\pm 5 m for each coordinate. Advise the farmer whether it is safe to construct a fixed-angle gate without first taking more precise on-site measurements. [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

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

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