The figures have different positions, different orientations, and different sizes. What transformations do you need to perform to undo such differences?
Example Solution: Translation → Rotation → Dilation
y= 7.5
z=9.6
Practice makes perfect
The two figures have different positions, different orientations, and different sizes. Therefore, to make them map onto each other, we have to perform a translation, a rotation and a dilation, not necessarily in that order, on one of the figures. If we start by performing a translation, we have to make two corresponding vertices, for example X and B, map onto each other.
Next, we want to rotate A'B'C'D' to give the figures the same orientation.
Finally, we will dilate A''B''C''D'' using B'' as the point of dilation. To determine the factor of dilation, we divide the length of a known side in WXYZ with its corresponding side in ABCD. For example, we know that ZY is 15 and the corresponding side in ABCD, is 6. With this, we can calculate the factor of dilation.
ZY/DC=15/6=2.5
Knowing the factor of dilation, we can perform a dilation and make the figures map onto each other.
Finding z and y
The ratio of the lengths of corresponding sides in similar figures is the same no matter which corresponding sides you use. With this we can write and solve two equations for z and y.
y/3&=15/6 ⇔ y= 7.5 [0.8em]
z/24&=6/15 ⇔ z=9.6
