Parallel Lines: Mixed Review
Mathematics
GCSE Higher
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A comprehensive worksheet reviewing the properties of parallel lines, focusing on loci and equidistant points, suitable for GCSE Higher students.
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Parallel Lines: Mixed Review
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concept below before attempting the questions.
1.
When two lines are parallel, the locus of points equidistant from both lines is a pair of lines parallel to them. The distance between these lines remains constant. Use this property to answer the questions below.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Construct a pair of parallel lines 8 cm apart. Draw the locus of points equidistant from both lines.
[3 marks]2.
Calculate the distance between two parallel lines given by equations y=3x+2 and y=3x-4.
[2 marks]3.
Given a line y=2x+1, find the equation of a line parallel to it that is 5 cm away.
[3 marks]4.
Plot the graph of y=2x and draw a line parallel to it that is 4 units above.
[3 marks]C
Problem Solving & Reasoning
Answer the following multi-step questions clearly.
1.
A line passes through the point (4, 3) and is parallel to the line y=5x-2. Find its equation and the distance from the point to the line.
[4 marks]2.
Two parallel roads are 120 meters apart. A drone flying at a height of 30 meters is located directly over a point on one of the roads. Find the shortest distance from the drone to the other road.
[4 marks]3.
A corridor is drawn parallel to a wall, 2.5 meters away. If the wall has the equation y=2x+1 and the corridor runs through point (3, 7), find its equation.
[3 marks]D
Real-world Applications
Apply your understanding to real-world scenarios.
1.
A railway track runs parallel to a river. The distance between the track and the river bank is 15 meters. If a bridge is to be built 10 meters away from the track, what is the minimum distance from the bridge to the river bank?
[3 marks]2.
In a city grid, two parallel streets are 50 meters apart. A new building is to be constructed 20 meters from one street, directly across from an existing building on the other street. Find the shortest distance between the two buildings.
[4 marks]E
Challenge & Extension
Attempt these more advanced problems.
1.
Prove that the locus of points equidistant from two parallel lines is a line parallel to both. Use algebraic methods.
[5 marks]2.
Given lines y=4x+1 and y=4x-3, find the coordinates of the point that is equidistant from both lines and lies directly between them on the perpendicular bisector.
[4 marks]F
Error Analysis
Identify and correct the common mistake in the following problem.
1.
A student claims that the distance between parallel lines y=2x+3 and y=2x-5 is 8 cm. Is this correct? If not, find the correct distance and explain the mistake.
[4 marks]Quick Actions
What is Remix?
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet