Question

question
the image point of a after a translation left 1 unit and up 4 units is the point b(6,11). determine the coordinates of the pre - image point a.
answer attempt 1 out of 2
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Explanation:

Step1: Recall translation rules

To find the pre - image, we reverse the translation. A translation left 1 unit and up 4 units was applied to the pre - image \(A=(x,y)\) to get the image \(B=(6,11)\). Reversing a left translation (subtraction of 1 from the x - coordinate) means we add 1 to the x - coordinate of the image. Reversing an up translation (addition of 4 to the y - coordinate) means we subtract 4 from the y - coordinate of the image.

Step2: Calculate the x - coordinate of A

For the x - coordinate: If the image \(x\) - coordinate is 6 and we had a translation left 1 unit (so \(x_{image}=x_{pre - image}- 1\)), then \(x_{pre - image}=x_{image}+1\). Substituting \(x_{image} = 6\), we get \(x=6 + 1=7\).

Step3: Calculate the y - coordinate of A

For the y - coordinate: If the image \(y\) - coordinate is 11 and we had a translation up 4 units (so \(y_{image}=y_{pre - image}+4\)), then \(y_{pre - image}=y_{image}-4\). Substituting \(y_{image}=11\), we get \(y = 11-4 = 7\).

Answer:

\((7,7)\)