Find the image of the point P(-11, -34) after 6 successive half turns about the point C(-11, 0)
To find the image of a point after several successive half turns, we can divide the turns into pairs and find the image after each pair of half turns.
Here, we have a point P(-11, -34) and the point C(-11, 0) as the center of rotation. We need to perform 6 successive half turns about C.
First, let's determine the vector from C to P. This can be done by subtracting the coordinates of C from the coordinates of P:
Vector CP = P - C = (-11 - (-11), -34 - 0) = (0, -34).
To perform a half turn about C, we rotate a point P by 180 degrees with respect to C. To rotate a point by 180 degrees, we simply negate both the x and y coordinates of the point.
So, the image of P after the first half turn is given by:
(-11 + 0, -34 + 0) = (-11, -34).
Now, let's consider the image of P after the second half turn. We take the image obtained after the first half turn and apply another half turn to it:
(-(-11), -(-34)) = (11, 34).
Similarly, we find the images after the successive half turns as follows:
Third half turn: (-11, 34).
Fourth half turn: (11, -34).
Fifth half turn: (-11, -34).
Sixth half turn: (11, 34).
Therefore, the image of the point P(-11, -34) after 6 successive half turns about the point C(-11, 0) is (11, 34).