Page 136 - Mathematics

(a) What are the coordinates of the points P, Q, and R?
(b) Find the gradients of PQ, PR, and QR.
(c) Write the name of the polygon formed by joining the points P,
Q, and R.

4. Catherine is a civil engineer who works at the road construction project.
The road needs to have a slope of 0.04 for proper drainage. If the horizontal
length is 600 metres, what should be the vertical length of elevation?
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5. The slope of the line joining the points (1, )p and (4, 2 )p is . Find
the value of p. 3
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6. Determine the nature of the straight line which passes through the points

K( 3, 2)− − and L(2, 1).

7. A line passes through points P(k, 4) and Q(3, k + 2). What value of k
will make the line to be (a) horizontal (b) vertical?
8. Calculate the gradient of each of the following pair of points and state
the nature of the line.
(a) (3, 6), ( 2, 1)− − (d) (2, 10), (2, 0)
(b) (0, 2), (6, 2) (e) (1, 0), (4, 0)
(c) ( 2, 3),− ( 1, 3)−−

9. The points A(3, ),y B (0, 4), and C( 2, 8)− are on the same straight line.
Determine the value of y.

10. Compare the values of the gradients of AB and PQ if the points

representing these lines are A(6, 4),− B(8, 4), P(6, 1), and Q(7, 5).
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11. A line joining (x, 0) and (5, − 2) has a slope of . Find the value of x.
4
12. Find the value of x so that the straight line joining the points (x, –5) and
(2, 1) has the same gradient as the line passing through points (1, 5) and
Mathematics Form One 13. Show whether line AB and PQ have the same gradients given that
−
( 2, 1).−

and Q( 4, 2).−
A( 3, 1), B (1, 2), P(0, 1),−

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25/10/2024 09:51:49
Mathematics form 1.indd 130
Mathematics form 1.indd 130 25/10/2024 09:51:49