Answer:
Step-by-step explanation:
The point A(-3,7) is first translated two units to the left and eight units down, resulting in a new point A'. Then, this new point A' is rotated about the origin by an angle of 90 degrees counterclockwise to produce the final image point A''.
To find the length of AA'', we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:
√((x2 - x1)^2 + (y2 - y1)^2)
First, we find the coordinates of A' after the translation:
A' = (-3 - 2, 7 - 8) = (-5, -1)
Then, we find the coordinates of A'' after the rotation:
A'' = (-1, 5)
Finally, we can calculate the length of AA'':
√((-1 - (-3))^2 + (5 - 7)^2)
= √(2^2 + (-2)^2)
= √(4 + 4)
= √8
= 2√2
Therefore, the length of AA'' is 2√2 units.
