Graph the image of C(
–
3,0) after a rotation 180° counterclockwise around the origin.
just change the sign of all coordinates
and review rotations
Sure, let's visualize that! Imagine you're at a circus, and there's a rotating clown act happening. So, the point C(-3,0) is our clown, ready for a twist!
Now, to rotate 180° counterclockwise around the origin, it's like spinning the clown really fast in the opposite direction as time goes back.
After this crazy maneuver, the clown point C(-3,0) will end up at the totally opposite spot, which is at (3,0). So, imagine the clown spinning around joyfully before landing at its new location, like a prank played on the audience! Voila!
To rotate a point counterclockwise around the origin, the x and y coordinates are switched with the sign of the new x-coordinate reversed.
Given the initial point C(-3, 0), we will switch the x and y coordinates and reverse the sign of the new y-coordinate.
Switching the coordinates, we get (0, -3). Then, reversing the sign of the new y-coordinate, we get (0, 3).
Therefore, the image of C(-3, 0) after a 180° counterclockwise rotation around the origin is (0, 3).
To graph this image, plot the point (0, 3) on the coordinate plane.
To graph the image of point C(-3,0) after a rotation of 180° counterclockwise around the origin, you can follow these steps:
1. Start by plotting the point C(-3,0) on the graph. This point represents the original position of C.
2. To rotate a point 180° counterclockwise around the origin, we need to swap the x and y coordinates of the original point and then negate both values.
- For the x-coordinate, swap -3 with 0 and negate the result: x' = -0 = 0.
- For the y-coordinate, swap 0 with -3 and negate the result: y' = -(-3) = 3.
So, the new coordinates of the point C after rotation are (0,3).
3. Plot the point (0,3) on the graph. This point represents the new position of C after a 180° counterclockwise rotation around the origin.
4. Connect the original point C(-3,0) and the new point (0,3) with a straight line. This line represents the path or trajectory followed during the rotation.
In summary, the point C(-3,0) after rotating 180° counterclockwise around the origin is located at (0,3).