Question

1. the area of \\( \triangle qrs \\) is 21 sq. ft. what is the area, in sq. ft, of the image of \\( \triangle qrs \\) after dilation with scale factor 2? 18. what is \\( eg \\)?

Explanation:

Step1: Recall the area - scale factor relationship

When a figure is dilated by a scale factor \(k\), the area of the new figure \(A'\) is related to the area of the original figure \(A\) by the formula \(A'=k^{2}A\). Here, the scale factor \(k = 2\) and the area of the original triangle \(A=21\) square feet.

Step2: Calculate the area of the dilated triangle

Substitute \(k = 2\) and \(A = 21\) into the formula \(A'=k^{2}A\). We get \(A'=(2)^{2}\times21\). First, calculate \(2^{2}=4\). Then, \(A'=4\times21\).

Answer:

\(84\)