Question

What is the image of the point (-7,9) after a rotation of 90^{\circ} counterclockwise about the origin?

a) (9,7)
b) (-9,-7)
c) (-9,7)
d) (7,-9)

Answer 1

After a 90° counterclockwise rotation around the origin, the point (-7,9) becomes (9,7). We switch the coordinates and change the sign of the original x-coordinate to get the new point.

Step-by-step explanation:

The question is asking for the image of the point after a rotation of 90° counterclockwise about the origin. To find this, we use the standard rules for 90° counterclockwise rotation, which are:

• The x-coordinate becomes the new y-coordinate, but with the opposite sign.
• The y-coordinate becomes the new x-coordinate.

Applying these rules to the point (-7,9), we get:

• New x-coordinate = 9 (since the original y-coordinate is 9).
• New y-coordinate = 7 (since the original x-coordinate is -7, and we change the sign).

Therefore, the image of the point after the rotation is (9,7), which corresponds to option a).