a The segments between the x-axis and the image and preimage corresponding vertices should be equal and perpendicular to the x-axis.
B
b Use a protractor to rotate the triangle.
C
c What can you say about the distance from the y-axis for corresponding points?
A
a A'(-2, -7)
B'(-5, -8)
C'(-3, -1)
B
b A''(2,7)
B''(5,8)
C''(3,1)
C
c Reflection in the y-axis.
Practice makes perfect
a Let's start by plotting △ ABC.
To reflect a point across the x-axis, we draw segments from the point towards, and perpendicular to, the x-axis.
By extending these segments to the opposite side of the x-axis, and with the same length as the first corresponding segment, we have reflected the points across the x-axis.
Finally, we will name the coordinates of the new vertices.
b To rotate a point by 180^(∘) about the origin, we draw segments from it and to the origin. Next, we use a protractor to draw a second segment that is at a 180^(∘) angle to the first segment. To find the coordinates of the rotated point, we have to make the second segment the same length as the first. Let's demonstrate with one of the points.
If we repeat the procedure for the remaining two points, we can draw the rotated triangle. Let's also name the coordinates of the new vertices.
c Let's compare △ ABC and △ A''B''C''
Examining the diagram, we see that A and A'' have the same vertical position and are equidistant from the y-axis. The same thing applies for B and B'' and for C and C''. Therefore, instead of the two transformations we did in Part A and Part B, we could have done a reflection in the y-axis instead.
