The gradients of several lines are as follows:

Question

Line a b c d e f g h
Gradient −3 0.5 0.4
(a) Find two pairs of lines that are parallel to each other.
(b) Find any two pairs of lines that are at right angles to each other.

Answer 1

(a) Two pairs of lines that are parallel to each other are:

Lines a and g both have a gradient of -3.

Lines b and c both have a gradient of 0.5.

(b) Two pairs of lines that are at right angles to each other are:

Lines a and f have gradients of -3 and 0.4, respectively. The product of their gradients is -3 * 0.4 = -1.2, which means they are perpendicular to each other.

Lines c and h have gradients of 0.5 and 0, respectively. The product of their gradients is 0.5 * 0 = 0, which means they are perpendicular to each other.