Find the coordinates of the image of point R(3,-5) rotated 180° about the origin.
To find the image of point R(3,-5) rotated 180° about the origin, we need to reflect the point across the x-axis and then the y-axis.
First, reflecting across the x-axis changes the sign of the y-coordinate, so R(3,-5) becomes R'(3,5).
Next, reflecting across the y-axis changes the sign of the x-coordinate, so R'(3,5) becomes R''(-3,5).
Therefore, the coordinates of the image of point R(3,-5) rotated 180° about the origin are (-3,5).
To find the coordinates of the image of point R(3, -5) rotated 180° about the origin, we can use the formula for rotating a point in a coordinate plane.
Here's how:
1. The rotation of 180° about the origin means that we need to find the point directly opposite R, on the other side of the origin.
2. To do this, we need to change the sign of both the x and y coordinates of point R.
So, the x-coordinate of the image will be -3 (the negation of 3), and the y-coordinate will be 5 (the negation of -5).
3. Therefore, the coordinates of the image of point R(3, -5) rotated 180° about the origin are (-3, 5).
To find the coordinates of the image of point R(3,-5) rotated 180° about the origin, we can use the following formula:
(x', y') = (-x, -y)
where (x', y') represents the coordinates of the image and (x, y) represents the coordinates of the original point.
Let's apply this formula to point R(3,-5):
x' = -3
y' = -(-5) = 5
Therefore, the coordinates of the image of point R(3,-5) rotated 180° about the origin are (-3, 5).