Page 135 - Mathematics_F1

Example 6.7

Show that a straight line passing through the points M(3,1) and N(3,4) is
vertical.
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Solution
Given the points M(3,1) and N(3,4). The gradient of the line joining the
two points is given by;

y − y
m = 2 1 . Let ( , ) (3, 1)xy = and ( ,xy ) (3, 4).=
x − x 1 1 1 2 2
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2
It follows that,
41
−
m =
3 3−
3
= which is undefined
0
Since the gradient of the line joining M and N is undefined, then the line MN
is vertical.

Example 6.8

Determine the nature of the straight line joining the points P(1, 2) and Q(5,2).

Solution
Given the points P(1, 2) and Q(5,2). The gradient of the line joining the
two points is given by;

y − y
m = 2 1 . Let ( , ) (1, 2)xy = and ( ,xy ) (5, 2).=
x − x 1 1 1 2 2
2
22−
Thus, m = 51−
Mathematics Form One Since the gradient of the line PQ is 0, then the nature of the line is horizontal.
0
=

4

0
=

128

25/09/2025 15:01:34
Mathematics form 1.indd 128
Mathematics form 1.indd 128 25/09/2025 15:01:34