Page 368 - Math Smart - 7

Using coordinates to describe transformations

You can describe the position of the object and the transformed Image using
coordinates on a coordinate grid.

The object and the image are points on the coordinate grid.

O Write down the coordinates of the object and the image.
Q State whether each statement is true or false.
a) The image is a translation of the object.
b) The image is a reflection of the object.
c) The image is a rotation of the object.

object im ige
—1 )—

The distance from the Solution
object to the image is 8
O Coordinates of the object: (-4, 3)
units, not 4 units.
Coordinates of the image: (4, 3)
Distance is counted from
0 True.
a)
one point to the other
The object has been translated by 8 units to the right.
point, not from the y-axis
The image is a translation of the object.
or x-axis.
We can also work out the
distance by finding the Ob ect im< ige
difference between their
x-coordinates:
Distance = 4-(-4)
= 4 + 4 -6-5 -4-3 -2 -1 0
= 8 units
b) True.
The object is 4 units to the left of the y-axis.
The image is 4 units to the right of the y-axis.
The objert has been reflected about the y-axis.
The image is a reflection of the object.

In this example, the line
line of reflection
of reflection is the y-axis.
ob ect im ige
However, an object and
an image can be reflected
along any line on the grid.

-6 -5 -4 -3 -2 -1 0

UNIT 16 I Transformation
E I