Page 130 - Mathematics_F1

Solution
(a) The gradient of the line joining B(1, 2) and C(0, 1)− is given by

y − y
m = 2 1 . Let ( , ) (0, 1)xy = − and ( ,xy 2 ) (1, 2).=
2
x − x 1 1 1
2
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Thus, m = 2 ( 1)− − Tanzania Institute of Education
10−
3
=
1

= 3
Therefore, the gradient of line BC is 3.

(b) The gradient of the line joining B (1, 2) and D (–1, – 4) is given by
y − y
m = 2 1 .
x − x 1
2
Let (x , y ) = (1, 2) and (x , y ) = (–1, – 4)
1
1
2
2
42
−−
Thus, m =
1 1
−−
− 6
=
− 2
= 3

Therefore, the gradient of BDis 3.

In this example, it can be observed that the gradient of a straight line does not
change when different pair of points are used provided that all the points lie on

the same line.

Mathematics Form One

123

25/09/2025 15:01:31
Mathematics form 1.indd 123
Mathematics form 1.indd 123 25/09/2025 15:01:31