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