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Contents
Parallel Lines
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Parallel
Lines
If
two lines are parallel, their gradients are equal.
Eg.
y = 2x + 1 is parallel to y = 2x + 3.
If
two lines are not parallel, there exist a point of intersection. This point
can be found by solving the two equations simultaneously.
 Example:
Determine whether the following pairs of lines are parallel. If there are not,
find their point of intersection.
(i) l1 : y = x + 3
l2 : the line joining A (1, 2) and B (-4, -3)
(ii) l3
: y = 2x + 7
l4
: the line joining C (5, 7) and D (-3, 6)
Solution:(i)
Gradient
of l1
= 1
Gradient
of l2
= [2-(-3)]/[1-(-4)] = 1
Since
the two gradients are the same, the pair of lines is parallel.
(ii)
Gradient
of l3
= 2
Gradient
of l4
= (7-6)/(5+3) = 1/8
Since
the two gradients are not the same, the lines are not parallel.
l4
: y - 7 = 1/8 (x-5)
8y = x + 51
Substitute
l3
into l4:
8 (2x + 7) = x + 51
15x = -5
x = -1/3
y = 19/3
The
coordinates of the point of intersection is (-1/3, 19/3)
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