**Problem 2** Select **all** of the pairs of polygons in which the image appears to be the result of a dilation of the pre-image. (*Select all that apply.*) **Description of Each Diagram:** 1. **Top Left Diagram:** - Shows two polygons with a series of dotted lines connecting corresponding vertices. The inner polygon appears smaller and is located inside the larger polygon. However, the shapes appear different, suggesting a transformation other than dilation. 2. **Top Right Diagram:** - Displays two polygons connected by dashed lines extending from a common external point (center of dilation). The smaller polygon is inside the larger one and maintains a similar shape, indicative of dilation. 3. **Bottom Left Diagram:** - Features two polygons in which a smaller polygon is nested within a larger one. Both polygons share a similar shape and are connected by lines drawn from each vertex of the inner polygon extending towards corresponding points on the outer polygon, suggesting dilation. 4. **Bottom Right Diagram:** - Two polygons are connected by dashed lines emanating from a point outside both polygons. The polygons have a different orientation and do not appear to maintain similarity in shape, indicating a transformation other than dilation. **Instructions for Solution:** Carefully analyze each pair of polygons to identify those that maintain proportionality and similarity indicating a dilation transformation. Select those that fulfill these criteria.

Use the Pythagorean Theorem to find the missing side for the right-angled triangle given in the figure below. It has base 112 m and height 15 m. If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -). 15 n 112 n • If you need to use the square root symbol, as in x = V17, type it using: sqrt(17) • Units need to be entered using their standard abbreviations, without a period. For example, type m for meters, m^2 for square meters, etc.

When a polygon reflects across the y-axis, how do the coordinates of the points change ?

Elementary school students were given a geometry assignment they were to measure the area of several rectangles to measure the diagonal of the rectangle as shown on the table.