Question

the triangle ( hij ) is a dilation of the triangle ( hij ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of \(IJ\)

The coordinates of \(I\) are \((3,3)\) and of \(J\) are \((1,3)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same), \(d=\vert x_2 - x_1\vert\). So \(IJ=\vert3 - 1\vert = 2\).

Step2: Find the length of \(I'J'\)

The coordinates of \(I'\) are \((6,9)\) and of \(J'\) are \((2,9)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same), \(d=\vert x_2 - x_1\vert\). So \(I'J'=\vert6 - 2\vert = 4\).

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\). So \(k=\frac{I'J'}{IJ}=\frac{4}{2}=2\).

Answer:

\(2\)