Question

ryan uses the following steps to describe the translation.
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?
step 1 step 2

Explanation:

Step1: Analyze Step 1

Step 1 correctly identifies the pre - image (triangle XYZ) and the image (triangle X'Y'Z'), so no error here.

Step2: Analyze Step 2

To determine the horizontal translation, we need to find the difference in the x - coordinates of corresponding points. Just stating "each point moves one unit left" without calculating the actual horizontal change between pre - image and image points is an error. We can't assume the horizontal translation is 1 unit left without proper calculation (finding the difference in x - coordinates of a point and its image, e.g., if \(X=(x_1,y_1)\) and \(X'=(x_2,y_2)\), horizontal translation is \(x_2 - x_1\)).

Step3: Analyze Step 3 (if needed)

But since we found an error in Step 2, we can conclude the first error is in Step 2.

Answer:

Step 2