Question

graph the image of the figure using the transformation given.

1. dilation of 1.5 about the origin
2. dilation of \\( \frac { 3 } { 2 } \\) about the origin

Explanation:

Step1: Recall the rule for dilation about the origin

When a figure is dilated about the origin with a scale factor \(k\), the coordinates of each point \((x,y)\) of the original figure are transformed to \((kx,ky)\). For problem 18, \(k = 1.5\), and for problem 19, \(k=\frac{3}{2}=1.5\). This means each coordinate of the vertices of the original figure is multiplied by the scale factor.

Step2: Analyze the size of the dilated figure

A dilation with a scale factor \(k> 1\) (in this case \(k = 1.5\)) enlarges the figure. Looking at the options for problem 18:

• Option A shows a figure that is smaller (if we assume the original figure has non - zero size, and the dilated figure with \(k = 1.5\) should be larger).
• Option B shows a larger figure.
• Option C has the orientation wrong (vertices are not in the correct relative positions after dilation).
• Option D is the same as the original (no dilation has occurred).

For problem 19:

• Option A shows a figure that is smaller.
• Option B shows a figure with the correct enlargement (since \(k=\frac{3}{2}=1.5\)).
• Option C shows a figure that is too large (if we consider the grid - based relative positions, it does not follow the \(k = 1.5\) rule).
• Option D is the same as the original (no dilation has occurred).

Answer:

1. B.
2. B.