Question

a) is scale drawing a an enlargement or a reduction of the original figure? b) what is the scale factor that relates scale drawing a to the original figure? c) is scale drawing b an enlargement or a reduction of the original figure? d) what is the scale factor that relates scale drawing b to the original figure? e) write an equation that relates the lengths of scale drawing b to the lengths of scale drawing a. let b represent a length of scale drawing b, and let a represent the corresponding length of scale drawing a.

Explanation:

Step1: Determine type of transformation for scale - drawing A

Compare size of scale - drawing A to original. Since scale - drawing A is smaller, it is a reduction.

Step2: Find scale factor for scale - drawing A

Let's assume we can count grid - squares. If the original has length \(l_{o}\) and width \(w_{o}\), and scale - drawing A has length \(l_{A}\) and width \(w_{A}\). If \(l_{o} = 4\) grid - squares and \(l_{A}=2\) grid - squares, the scale factor \(k_{A}=\frac{l_{A}}{l_{o}}=\frac{2}{4}=\frac{1}{2}\).

Step3: Determine type of transformation for scale - drawing B

Compare size of scale - drawing B to original. Since scale - drawing B is larger, it is an enlargement.

Step4: Find scale factor for scale - drawing B

If the original has length \(l_{o} = 4\) grid - squares and scale - drawing B has length \(l_{B}=8\) grid - squares, the scale factor \(k_{B}=\frac{l_{B}}{l_{o}} = 2\).

Step5: Write equation relating lengths of scale - drawing B and A

Let \(b\) be a length of scale - drawing B and \(a\) be the corresponding length of scale - drawing A. Since \(k_{B}=2\) and \(k_{A}=\frac{1}{2}\), and \(b = k_{B}\times l_{o}\), \(a = k_{A}\times l_{o}\), then \(b = 4a\) (because \(\frac{b}{a}=\frac{k_{B}}{k_{A}}=\frac{2}{\frac{1}{2}} = 4\)).

Answer:

a. Scale - drawing A is a reduction.
b. Scale factor of scale - drawing A to original is \(\frac{1}{2}\).
c. Scale - drawing B is an enlargement.
d. Scale factor of scale - drawing B to original is \(2\).
e. Equation relating lengths: \(b = 4a\)