Question

1. the image point of a after a translation left 1 unit and down 1 unit is the point b(0, -7). determine the coordinates of the pre - image point a.

Explanation:

Step1: Analyze the translation rules

Translation left 1 unit means subtract 1 from the x - coordinate and down 1 unit means subtract 1 from the y - coordinate. To find the pre - image, we do the opposite operations.

Step2: Find the x - coordinate of point A

Let the coordinates of point A be $(x,y)$. Since the x - coordinate of the image B is 0 and the translation in the x - direction is left 1 unit (subtract 1), to get the pre - image x - coordinate we add 1. So $x=0 + 1=1$.

Step3: Find the y - coordinate of point A

Since the y - coordinate of the image B is - 7 and the translation in the y - direction is down 1 unit (subtract 1), to get the pre - image y - coordinate we add 1. So $y=-7 + 1=-6$.

Answer:

$(1,-6)$