If triangle ABC shown in the figure below is reflected about the y-axis what would the coordinates of the new triangle vertices be?
a. (-3, 3) (-5, 6) (-5, 3)
b. (-3, -3) (-5, -6) (-5, -3)
c. (3, -3) (6, -5) (3, -5)
d. (-3, -3) (-6, -5) (-3, -5)
Answer: (a) (-3, 3) (-5, 6) (-5, 3)
In order to solve this problem, it is important to understand what happens when an object is reflected about an axis. When an object is reflected about an axis the vertices of the new object will have the same distance from that axis like the original object.
The reflection of triangle ABC is done about the y-axis in this problem. Therefore, the distances each ordered pair has from the y-axis will be the same in the new triangle. This means that the y-coordinate of each ordered pair will be the same in the new triangle like they are in triangle ABC. However, the reflection will mean that the x-coordinates of these points will have the opposite sign in the new object from the original one. In this case, the positive x-coordinates will change to negative x-coordinates.
To simplify this, we’ll look at the location of each ordered pair in the original triangle as follows:
Ordered pair (A) has the original points of (3, 3) therefore the reflected pair will be (-3, 3)
Ordered pair (B) has the original points of (5, 6) therefore the reflected pair will be (-5, 6)
Ordered pair (C) has the original points of (5, 3) therefore the reflected pair will be (-5, 3)
Note in all of the above points, the x-coordinate changed from a positive to a negative while the y-coordinate remained unchanged.
© Copyright 2008.Najwa S. Hirn. All rights reserved.
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