b Draw a perpendicular segment from each vertex to l. Extend these segments on the opposite side of l until they are congruent with the first segment.
C
c How many steps do you have to move in x and y to get to the specified point. All points have to move the same way when translating the triangle.
A
a C'=(-6,-3)
B
b A''=(6,2), B''=(2,3) and C''=(5,6)
C
c B'''=(8,- 4)
Practice makes perfect
a To rotate the triangle 90^(∘) counterclockwise around the origin, we need a protractor. First we draw segments from each vertex to the origin. Then, place the center of the protractor at the origin and line it up along one of these segments. By drawing a congruent segment from the origin and along the 90^(∘) mark on the protractor, we will have located one of the rotated points.
If we repeat this process for all vertices and connect the rotated points, we can draw △ A'B'C'.
Now we can directly identify the coordinates for C'.
C'(-6,-3)
To reflect the triangle across x=1, we have to draw perpendicular segments from each vertex to x=1. By extending these segments on the opposite side of x=1, until they reach the same length as their corresponding first segment, we have found the position of the reflected points.
We have now plotted all the reflected points. Finally, we will connect these points in order to graph the reflected triangle △ A''B''C''.
The coordinate of the image vertices are A''(6,2), B''(2,3) and C''(5,6).
c If we want to translate A to (4,-5) we must move the vertex to the right by 8 steps and down by 7 steps.
To complete the transformation, we want to translate the remaining vertices the same way.
Now we can directly identify the coordinates for B'''.
B'''(8,-4)
