What is the final position of point A(7, 8) after a translation of 2 units left, 1 unit down, and followed by a 180-degree clockwise rotation around the origin?

Question

A' =

Answer 1

To find the final position of point A after the translation and rotation, we need to perform the operations in the given order.

Translation 2 units left and 1 unit down:
A' = (7-2, 8-1) = (5, 7)

Now, the new position of A' is (5, 7). To perform a 180-degree clockwise rotation around the origin, we need to reflect the point across the x-axis and then across the y-axis.

The x-coordinate of A' remains the same, but the sign of the y-coordinate changes:
A' = (5, -7)

Therefore, the final position of point A after a translation of 2 units left, 1 unit down, and a 180-degree clockwise rotation around the origin is A' (5, -7).

Answer 2

Its actually (-5, -7)

Answer 3

Apologies for the mistake in my previous response. Let's correct it:

After the translation 2 units left and 1 unit down, the new position of point A is (5, 7).

Now, to perform a 180-degree clockwise rotation around the origin, we need to reflect the point across both the x-axis and y-axis.

Reflecting across the x-axis: (5, 7) → (5, -7)
Reflecting across the y-axis: (5, -7) → (-5, -7)

Therefore, the final position of point A after a translation of 2 units left, 1 unit down, and a 180-degree clockwise rotation around the origin is A' (-5, -7). Thank you for pointing out the error.