What is the new point after rotating the point (3,−5) 180° clockwise?
To rotate a point 180° clockwise, we need to change the sign of both the x-coordinate and the y-coordinate.
The original point is (3,-5).
After rotating 180° clockwise, the new point would be (-3, 5).
If a segment has endpoints (0, 4) and (3, 4) , how long will the segment be after it is rotated 270° clockwise?
To find the length of the segment after rotating it 270° clockwise, we first need to determine the new coordinates of the endpoints after the rotation.
When a point is rotated 270° clockwise, the x-coordinate becomes the negative value of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.
The original endpoints are (0, 4) and (3, 4).
After rotating 270° clockwise, the new endpoints would be (4, 0) and (4, -3).
To find the length of the segment, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of the new endpoints, the length of the segment after the rotation would be:
Distance = √((4 - 4)^2 + (0 - (-3))^2)
= √(0 + 9)
= √9
= 3
So, the length of the segment after rotating it 270° clockwise is 3 units.
A square with sides 6 units in length is reflected across the x -axis. How long are the sides in the reflected figure?
When a square is reflected across the x-axis, the y-coordinates of its vertices are negated. The x-coordinates remain the same.
Let's consider a square with sides of length 6 units.
The vertices of the square are: (0,0), (6,0), (6,6), and (0,6).
When we reflect the square across the x-axis, the y-coordinates of each vertex become negated.
Thus, the reflected figure has the following vertices: (0,0), (6,0), (6,-6), and (0,-6).
The length of the sides in the reflected figure can be determined by finding the distance between two adjacent vertices.
For example, the distance between (0,0) and (6,0) is 6 units. Similarly, the distance between (6,0) and (6,-6) is also 6 units.
Therefore, the sides of the reflected square are each 6 units in length.