Sign In
What transformation maps a figure onto another if they do not have the same size?
Example Transformation Sequence: Translation followed by dilation
Missing Side Measure: x=16.25
We are given two similar polygons and want to determine the transformations that map one figure onto the other. Then we want to find the missing side measure.
We will do these things one at a time.
Since the figures are similar, they have the same shape but they do not have the same size. Let's determine what transformations map one onto the other.
A translation followed by a dilation maps the first quadrilateral onto the second.
Because the figures are similar, the ratio of the corresponding side measures is constant. Therefore, to find the missing side measure we will set up a proportion. 26/x=12/7.5 Let's solve the equation! Our first step in solving is to remove the denominators from both sides of the equation using the Multiplication Property of Equality.
LHS * x=RHS* x
a/x* x = a
a/c* b = a* b/c
LHS * 7.5=RHS* 7.5
Multiply
a/7.5* 7.5 = a
Rearrange equation
Finally, we can isolate x using the Division Property of Equality.
.LHS /12.=.RHS /12.
Split into factors
a* b/c=a/c* b
a/a=1
Identity Property of Multiplication
Calculate quotient