Question

n rule (x, y) → (x + 4, y + 7) slide of the pre-image (4, 5) as his error? sample response: the pre-image is the point you start with. to check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. you get (4, 5) → (4+4, 5+7). simplify to get (4, 5) → (8, 12). this is the image. instead the rule was applied to the image. this is the source of the error. what did you include in your response? check all that apply. ☐ the transformation rule should be applied to the pre-image. ☐ the application of the rule results in the point (8, 12). ☐ the transformation rule was applied to the wrong point.

Explanation:

1. The transformation rule \((x,y)\to(x + 4,y + 7)\) should be applied to the pre - image (the original point, here \((4,5)\)). So the option "The transformation rule should be applied to the pre - image" is correct.
2. When we substitute \(x = 4\) and \(y=5\) into the rule \((x,y)\to(x + 4,y + 7)\), we get \(x+4=4 + 4=8\) and \(y + 7=5+7 = 12\), so the image is \((8,12)\). Thus the option "The application of the rule results in the point \((8,12)\)" is correct.
3. The error occurred because the rule was applied to the image instead of the pre - image, which means the transformation rule was applied to the wrong point. So the option "The transformation rule was applied to the wrong point" is correct.

Answer:

• The transformation rule should be applied to the pre - image.
• The application of the rule results in the point \((8,12)\).
• The transformation rule was applied to the wrong point.