Question

ryan wants to describe the translation shown on the grid.
ryan uses the following steps to describe the translation.
ryans work
step 1: identify the pre - image and the image:
the pre - image is triangle xyz, and the image is xyz.
step 2: identify the number of units that each point moves horizontally:
each point moves one unit left.
step 3: identify the number of units that each point moves vertically:
each point moves three units down.
step 4: the translation is one unit left and three units down.
in which step did ryan make the first error?

Explanation:

Step1: Analyze Step 2

In a translation, we look at the horizontal and vertical shifts. For horizontal shift: count how many units a point moves left/right. If we take a corresponding point from pre - image to image (e.g., \(Z\) to \(Z'\)), the horizontal movement is \(3\) units right (not \(1\) unit left as Ryan said in Step 2).

Step2: Analyze other steps

Step 1: Correctly identifying pre - image (\(XYZ\)) and image (\(X'Y'Z'\)). Step 3: For vertical movement (e.g., \(Z\) to \(Z'\)), if we consider the \(y\) - coordinates, it is \(3\) units up (not down as in Step 4). But the first error is in Step 2.

Answer:

Step 2