Question

The line l is perpendicular to line m.

a) Is CE= EG?
b) Does PE bisect CG?
c) Identify any two line segments for which PE is the perpendicular bisector.
[3 MARKS]

Answer 1

Each Option: 1 Mark

Given that:
Line l is perpendicular to line m.
a) We can clearly see from the above diagram that CE = 5-3 = 2 units
Also, EG = 7-5 = 2 units
$\therefore$ CE = EG = 2 units
b)As we have seen above CE = EG
So, E is the mid-point of line CG.
$\therefore$ Line PE bisects CG.

c) We can see from the above figure that
BE = 5-2 = 5 units
HE = 8-5 = 3 units
$\therefore$ E is the mid-point of the line BH.
Also given that line m is perpendicular to the line l.
$\therefore$ PE is the perpendicular bisector of the line segment BH.
Also, we have seen above that PE is also the perpendicular bisector of line segment CG.
$\therefore$ The required line segments are BH and CG.