This chapter requires very little new material and much of it relies simply on Pythagoras’
theorem.
7.1 Review
7.1.1 Coordinate systems in a plane ➤205 220➤➤
A.Plot the points with Cartesian coordinates
(i) (0, 0) (ii) (0, 1) (iii) (−1, 3)
(iv) (−2, 4) (v) (− 2 ,− 3 ) (vi) (0,−1)
(vii) (3, 3) (viii) (3,−2)
B. Plot the points with polar coordinates (r, θ)
(i) (0, 0) (ii) (0,π) (iii) (1, 0) (iv)
(
1 ,
π
2
)
(v)
(
3 ,−
π
2
)
(vi)
(
2 ,
π
6
)
(vii)
(
6 ,
5 π
4
)
(viii)
(
5 ,
2 π
3
)
7.1.2 Distance between two points ➤208 221➤➤
Find the distance between the following pairs of points referred to rectangular Carte-
sian axes.
(i) (0, 0), (1, 1) (ii) (1, 2), (1, 3) (iii) (−2, 4), (1,−3)
(iv) (− 1 ,− 1 ),(− 2 ,− 3 )
7.1.3 Midpoint and gradient of a line ➤209 221➤➤
Find the (a) mid-point and (b) the gradient of the line segments joining the pairs of points
in Question 7.1.2.
7.1.4 Equation of a straight line ➤212 221➤➤
A.Determine the equations of the straight lines through the pairs of points in
Question 7.1.2.
B.Find the gradient and the intercepts on the axes of the lines
(i) y= 3 x+ 2 (ii) 2x+ 3 y= 1 (iii) y= 4 x
(iv) x+y+ 1 = 0