Rotate a point on a line at (−4, 6) 180° counterclockwise. What is the resulting point?
To rotate a point 180° counterclockwise, we can simply change the sign of both the x-coordinate and the y-coordinate of the point.
The given point is (-4, 6).
To rotate it 180° counterclockwise, we change the sign of both coordinates:
-4 becomes 4, and
6 becomes -6.
Therefore, the resulting point after rotating (-4, 6) 180° counterclockwise is (4, -6).
Jack discovers that the orientation of a triangle is counterclockwise. He then reflects the triangle over the y -axis. What is the orientation of the reflected figure?
When a figure is reflected over the y-axis, the orientation of the figure remains the same. Since the original triangle was counterclockwise, the orientation of the reflected triangle will also be counterclockwise.
Jack discovers that the orientation of a triangle is counterclockwise. He then reflects the triangle over the y-axis. What is the orientation of the reflected figure?
There is not enough information to tell.
The reflected figure has a counterclockwise orientation.
The reflected figure has a clockwise orientation.
The orientation could be clockwise or counterclockwise depending on how you do the reflection.
The correct answer is: The orientation could be clockwise or counterclockwise depending on how you do the reflection.
If a triangle with vertices (4, 3) , (8, 3) , and (7, 5) is translated to the right 4 units and down 2 units, what are the vertices of the translated figure?
To translate a figure, we add the same amount to the x-coordinate and y-coordinate of each vertex.
The given triangle has vertices at (4, 3), (8, 3), and (7, 5).
To translate the triangle to the right 4 units and down 2 units, we add 4 to each x-coordinate and subtract 2 from each y-coordinate:
(4, 3) + (4, -2) = (8, 1)
(8, 3) + (4, -2) = (12, 1)
(7, 5) + (4, -2) = (11, 3)
Therefore, the vertices of the translated triangle are (8, 1), (12, 1), and (11, 3).
Which transformation(s) will result in a figure that has the same orientation as the original figure?
translation only
translation, rotation, and reflection
reflection only
translation and rotation