Question

problem 8. here is triangle abc. drag the points to dilate each vertex of triangle abc using point p as the center of dilation and a scale factor of 2. here is your graph from the previous screen. if the length of side ab is 4.5 units and the length of side bc is 4.1 units, what are the lengths of side ab and side bc? ab bc

Explanation:

Step1: Recall dilation formula

The formula for dilation of a line - segment length is \(L'=kL\), where \(L'\) is the length of the dilated line - segment, \(L\) is the original length, and \(k\) is the scale factor. Here, \(k = 2\).

Step2: Calculate length of \(A'B'\)

Given the length of side \(AB\) is \(4.5\) units. Using the dilation formula \(L'=kL\), with \(k = 2\) and \(L = 4.5\), we have \(A'B'=2\times4.5=9\) units.

Step3: Calculate length of \(B'C'\)

Given the length of side \(BC\) is \(4.1\) units. Using the dilation formula \(L'=kL\), with \(k = 2\) and \(L = 4.1\), we have \(B'C'=2\times4.1 = 8.2\) units.

Answer:

\(A'B' = 9\) units, \(B'C'=8.2\) units