Page 171 - Mathematics

18. (a) Draw the graph of a straight line y = 3x + 5. By using construction

method, draw a line perpendicular to the line drawn in (a) at
point (0, 5).
(b) Calculate the slope of the line drawn in (b).
(c) How are the slopes in (a) and (b) related? Tanzania Institute of Education
(d) Measure and record the angle between the lines.
(e) What conclusion can you make about the product of the gradients of
the two perpendicular lines?
19. Without drawing a graph, find the point of intersection between a line
passing through the points (0 1) and (3, 7) and a line y = 4x + 7.
20. Find the value of x so that A (1, 3), B( 2, 3),−− and C( ,7)x are the points
on the same straight line.
21. Which of the following points lie on the line 3x + 4y − 12 0?=
(a) A(0, 2) (b) B(4, 0) (c) C(2, 4)

 4 
(d) D  ,2 (e) E(–3, 2)

 3 
22. (a) Points A, B, and C are the vertices of a right-angled triangle at C. If
the coordinates of A and C are A(0, 3) and C(5, 7)− − , what are the
coordinates of point B?
(b) A parallelogram ABCD has vertices at A(1, –3), B(6, –2), C(3, 4),

and D(x, y). What are the coordinates of vertex D?
23. Find the equation of a line whose y-intercept is the same as the that of
a line 4x y+ + 60= and the product of their gradients is 1.−
24. A line through the point (3, 1) has the same gradient as the line
16x − 4y = 23. Find the equation of the line.
25. Two roads whose equations are 2x + 3y = 7 and x − 3y += intersect
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at point P. A new road is to be constructed from A (5, 5) to point P. Find
the equation of the new road in the form ax by+ = . c

26. The line passing through A (1, k) and B(k + 9, 2)− has the same gradient
as the line passing through C (3, 4) and D( 2,3).− Find the value of k.
27. A doctor advice the patient to take 500 mg of calcium and 1,200
micrograms of vitamin A by drinking milk and orange juice. A unit of
milk contains 38 mg of calcium and 56 micrograms of vitamin A while Mathematics Form One
a unit of orange juice contains 5 mg of calcium and 60 micrograms of
vitamin A. How many units of each should the patient take?

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25/10/2024 09:52:07
Mathematics form 1.indd 165
Mathematics form 1.indd 165 25/10/2024 09:52:07