Question

ac = 4 units
what is the length of bc, the image of segment bc?
bc = units

Explanation:

Step1: Count the length of \(AC\) and \(BC\)

From the graph, \(AC = 8\) units. Given \(A'C=4\) units. So the scale factor \(k=\frac{A'C}{AC}=\frac{4}{8}=\frac{1}{2}\). Also, from the graph \(BC = 10\) units.

Step2: Calculate \(B'C\)

Since the transformation is a dilation (assuming a similarity transformation as lengths are scaled proportionally), if the scale factor is \(k\), then for a segment \(BC\) and its image \(B'C\), the formula is \(B'C=k\times BC\). Substituting \(k = \frac{1}{2}\) and \(BC = 10\) into the formula, we get \(B'C=\frac{1}{2}\times10\).

Answer:

\(5\)