Question

quadrilateral hijk is dilated by a scale factor of \\(\frac{3}{4}\\) to form quadrilateral hijk. what is the measure of side kh?
image of quadrilateral hijk with side kh = 8, hi = 16, ij = 16, jk = 17.9, and hi, ij are horizontal and vertical respectively
answer attempt 1 out of 2

Explanation:

Step1: Recall the dilation formula

When a figure is dilated, the length of a side of the new figure is equal to the scale factor multiplied by the length of the corresponding side of the original figure. The formula is \( \text{Length of new side}=\text{Scale factor}\times\text{Length of original side}\).

Step2: Identify the original side and scale factor

The original side \(KH = 8\), and the scale factor is \(\frac{3}{4}\).

Step3: Calculate the length of \(K'H'\)

Substitute the values into the formula: \(K'H'=\frac{3}{4}\times8\). Using the rule of fraction - multiplication \(a\times\frac{b}{c}=\frac{a\times b}{c}\), we have \(K'H'=\frac{3\times8}{4}\). Since \(8\div4 = 2\), then \(3\times2=6\).

Answer:

\(6\)