Page 132 - Mathematics Coursebook

13.2 Lines parallel to the axes

13.2 Lines parallel to the axes y
2
A
1
On this grid, the red line through A(4, 1) and B(4, −5) has been 0 x
extended in both directions. –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6

Some other points on the red line are: –2
–3
(4, 3) (4, 5) (4, −3) (4, 0) (4, −4) (4, 2) (4, −6) –4

"ey all have an x-coordinate of 4. Every point with an –5 B
x-coordinate of 4 will be on this line. –6
An equation is like a rule connecting x and y. " e equation of the

red line is x = 4. "e line x = 4 is perpendicular to the x-axis and You learnt about equations in
passes through the 4 on the x-axis. Units 2 and 9.

"e diagram also shows the lines x = 2 and x = −5.
y

"e equation of the y-axis is x = 0. 3
"ese points are on the blue line drawn here: 2

1
(5, 3) (−4, 3) (2, 3) (−2, 3) (0, 3) 0 x
–6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6
"e y-coordinate of points on this line is always 3.

–2

"e equation of the blue line is y = 3. –3
"e equations of the other lines are y = −2 and y = −5. –4

–5
"e equation of the x-axis is y = 0.

) Exercise 13.2

1 Find the equation of the line through these points. y
a P and Q b Q and R c R and S d S and T 6
5
2 a On a coordinate grid, draw and label the lines x = 7 and T 4
y = −4. 3
b Write down the coordinates of the point where P 2 Q
the lines cross. 1
3 a On a coordinate grid, draw the rectangle with corners at –6 –5 –4 –3 –2 –1 –1 0 1 2 3 4 5 6 x
A(2, 7), B(−6, 7), C(−6, 1) and D(2, 1). –2
b Write down the equation of the line through B and C. S –3 R
c Write down the equation of the line through A and B. –4
d The rectangle has two lines of symmetry. Write down the –5
–6
equation of each of them.
4 Find the equation of the line through these points.
a (4, −5) and (4, 2) b (−3, 6) and (3, 6) c (−5, 5) and (−5, 0)

5 Three of these points are in a straight line.
Find the equation of the line. (4, 2) (2, 4) (−2, 4) (−4, 2) (−4, −2) (2, 2)

6 A rhombus has vertices at the points (−2, 8), (1, 2), (−2, −4) and (−5, 2).
a Draw the rhombus.
b The rhombus has two lines of symmetry. Write down the equations of these lines.

13 Graphs 131