HIGHER MATHEMATICS
THE STRAIGHT LINE: END OF TOPIC
1.
A is the point (2, 3) and B is (4, 5).
(a)
(b)
(c)
.
2.
Find the equation of AB.
Find the length of AB.
Calculate the angle a , to the nearest degree.
Prove that the line y  2 x  1 is perpendicular to the line 3 x  6 y  1 .
What is the gradient of the line 2 y  3x  12  0 ?
The line 2 y  3x  12  0 crosses the y -axis at A and the x -axis at B.
Find the coordinates of A and B.
3.
(a)
(b)
4.
A is the point (4, 1), B is (2, 
5.
6.
1
) and C is (12, 3).
2
Prove that the points A, B and C are collinear.
Find the coordinates of the point of intersection of the lines y  2 x  3 and
3x  y  2 .
(a)
(b)
(c)
7.
3
passing through the point
4
(4, 1).
Find the equation of the line passing through the points (7, 3) and
(10, 1).
Prove that the two lines in (a) and (b) are perpendicular, and find their
point of intersection.
A(0, 2), B(3, 7) and C(9, 5) are vertices of rectangle ABCD.
Find:
8.
Find the equation of the line with gradient
(a)
(b)
the equations of sides AD and CD
the coordinates of D.
The equations of the sides of triangle PQR are:
PQ: 4 y  x  11
QR: y  x  1
PR: y  2 x  4
Find the coordinates of P, Q and R.
9.
In triangle STU, S is (2, 6), T is (4, 2) and U is (13, 7).
(a)
(b)
(c)
Find the equation of the altitude SF.
Find the equation of the median UE.
Find the coordinates of the point of intersection of SF and UE.
10.
Find the gradient of the line joining the points:
(a)
A(1, 3) and B(4, 9)
(b)
P(4, 1) and Q(2, 4)
(c)
K(0, 7) and L(6, 3)
(d)
E(3, 5) and F(1, 3)
11.
A is the point (2, 5), B is (6, 7), C is (9, 2) and D is (1, 0).
Prove that ABCD is a parallelogram.
12.
Prove that the points A(4, 3), B(2, 1) and C(14, 3) are collinear.
13.
Find the gradient of the line below.
Give your answer correct to 1 decimal place.
y
O
35
x
14.
Find the angle that the line joining K(2, 3) and L(4, 7) makes with the positive
direction of the x -axis.
15.
P is the point (2, 6) and Q is the point (1, 3).
Find the gradient of a line:
(a)
parallel to PQ
(b)
perpendicular to PQ.
16.
Triangle KLM has vertices K(1, 2), L(1, 7) and M(4, 0).
Prove that the triangle is right-angled.
17.
At 1300 hours a ferry is located at the point (5, 2) relative to coordinate
axes. The ferry sails on a straight line course and one hour later is at the point
(1, 0). If the ferry continues on the same course, will it collide with a
stationary fishing vessel located at the point (1, 1)?