Example 4
Draw the following points on graph paper:
a. A(1, 3)
b. B(5, 3)
c. C(5, 7)
d. D(1, 7)
Join the points A, B, C and D in alphabetical
order; and describe the pattern you have drawn.
Solution:
If we join the points A to B, B to C, C to
D and D to A, we obtain a square of side-length 4
units.
Linear Patterns
A linear pattern is formed when all of the points examined lie in
a straight line.
Example 5
a. Plot the following points on a Cartesian plane:
A(0, 5), B(1, 5), C(2, 5),
D(3, 5), E(4, 5), F(5, 5), G(6, 5), H(7,
5)
Use a ruler to join the points A, B, C,
D, E, F, G and H.
b. Describe the linear pattern in words.
c. If the linear pattern is extended, find the y-coordinate of
the point whose x-coordinate is 8.
d. If the linear pattern is extended, does the point (10, 5) lie on
the line?
e. If the linear pattern is extended, does the point (5, 15) lie on
the line?
Solution:
b. The y-coordinate of any point in this linear pattern is
always 5.
c. When x = 8, y = 5.
d. (10, 5) is on the line because the y-coordinate is always 5.
e. (5, 15) does not lie on the line because its y-coordinate is
not 5.
Example 6
a. Plot the following points on a Cartesian plane:
A(5, 1), B(5, 2), C(5, 3),
D(5, 4), E(5, 5), F(5, 6)
Use a ruler to join the points A, B, C,
D, E and F.
b. Describe the linear pattern in words.
c. If the linear pattern is extended, does the point (10, 5) lie on
the line?
d. If the linear pattern is extended, does the point (5, 15) lie on
the line?
Solution:
b. In this linear pattern, the x-coordinate of any
point is always 5.
c. (10, 5) does not lie on the line because the x-coordinate is
not 5.
d. (5, 15) is on the line because the x-coordinate is 5.
Key Term
linear pattern
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