Question

tia used a photocopier to dilate the design for a monorail track system. the figure shows the design and its photocopy. the ratio of da:he is 1:2. what is the length, in meters, of side fg on the photocopied image? 14 17 28 34

Explanation:

Step1: Identify similar - figures property

Dilation creates similar figures. Corresponding sides of similar figures are in proportion.

Step2: Determine the proportion relationship

Since the ratio of DA:HE is 1:2, all corresponding sides of the original design and the photocopy are in the ratio 1:2.

Step3: Find the length of FG

Side AB in the design corresponds to side FG in the photocopy. AB = 17 m. Using the ratio 1:2, if the side in the original is \(x\) and in the copy is \(y\), then \(\frac{x}{y}=\frac{1}{2}\). For AB and FG, if \(x = 17\) m, then \(y=2x\). So \(FG = 2\times17=34\) m.

Answer:

34