Question

a dilation maps \\( \triangle hij \\) onto \\( \triangle h ^ { \prime } i ^ { \prime } j ^ { \prime } \\). find the missing values.
\\( hi = 5 \\) in \\( h ^ { \prime } i ^ { \prime } = 20 \\) in
\\( ij = 2 \\) in \\( i ^ { \prime } j ^ { \prime } = \square \\) in
\\( hj = 6 \\) in \\( h ^ { \prime } j ^ { \prime } = \square \\) in
(simplify your answers.)

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of the dilation is given by the ratio of the corresponding sides \(H'I'\) and \(HI\).

$$k=\frac{H'I'}{HI}$$

Substitute \(H'I' = 20\) in and \(HI = 5\) in.

$$k=\frac{20}{5}=4$$

Step2: Calculate \(H'J'\)

Since \(H'J'=k\times HJ\), and \(HJ = 6\) in, \(k = 4\)

$$H'J'=4\times6 = 24$$

Step3: Calculate \(I'J'\)

Since \(I'J'=k\times IJ\), and \(IJ = 2\) in, \(k = 4\)

$$I'J'=4\times2=8$$

Answer:

\(H'J' = 24\) in, \(I'J'=8\) in