Author: Stewart Gale

Exam Questions – Parallel and Perpendicular Lines

Q1.
Find an equation of the straight line that is perpendicular to the straight line 
x + 2y = 5 and that passes through the point (3, 7).

(Total for Question is 4 marks)
Q2.

ABCD is a square. 
P and D are points on the y-axis.
A is a point on the x-axis. 
PAB is a straight line.
The equation of the line that passes through the points A and D is y = –2x + 6
Find the length of PD.

 

  

(Total for Question is 4 marks)
Q3.
 
ABCD is a rectangle.
A, E and B are points on the straight line L with equation x + 2y = 12 
A and D are points on the straight line M.
AE = EB
Find an equation for M.

 
(Total for question = 4 marks)
Q4.
 
In the diagram
A is the point (0, 4) 
B is the point (6, 0)
M is the midpoint of AB.
Find an equation of the line that passes through M and is perpendicular to AB.

(Total for question = 4 marks)
 Q5.

ABCD is a rhombus. The coordinates of A are (5,11) 
The equation of the diagonal DB is y = ½x + 6 
Find an equation of the diagonal AC.

 

(Total for question = 4 marks)
 Q6.
 P has coordinates (–9, 7) 
Q has coordinates (11, 12)
M is the point on the line segment PQ such that PM : MQ = 2 : 3
Line L is perpendicular to the line segment PQ. 
L passes through M.
Find an equation of L.

 
(Total for question = 5 marks)
 Q7.

The point A has coordinates (2, 5). 
The point B has coordinates (4, 9).
The line L passes through the points A and B. 
The equation of line L is y = 2x + 1
M is the midpoint of the line segment AB.
Find an equation of the line that is perpendicular to line L and passes through M.

 
(Total for question = 4 marks)
 Q8.
 A(−2, 1), B(6, 5) and C(4, k) are the vertices of a right-angled triangle ABC. 
Angle ABC is the right angle.
Find an equation of the line that passes through A and C. 
Give your answer in the form ay + bx = c where a, b and c are integers.

  
(Total for question = 5 marks)