1.A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?(1 point)
2.A line segment has endpoints (2,−1) and (5, −4) . What are the new endpoints after rotating the segment 90° clockwise?(1 point)
3.A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?(1 point)
4.Translate the figure HIJKL 3 units to the left. Which of the following would be a vertex in the translated figure?
(1 point)
5.Triangle XYZ is translated down 4 units and to the left 8 units. The length of side XY is 10 units. What is the length of side X′Y′ ?(1 point)
6.Triangle MNO is translated up 5 units and left 2 units. Point N is located at (0, −6) . What are the coordinates of N′ ?(1 point)
7.The shape of a heart is reflected across the x -axis. If the point at the bottom of the heart for the original figure is at (314,712) , what are the coordinates for the point at the bottom of the heart in the reflected image?(1 point)
8.A four-sided figure WXYZ is shown on the coordinate plane. The figure is then reflected across the y -axis. Which point of the figure above will end up in Quadrant I?
9.Reflect square ABCD with respect to the x -axis and the y -axis. What are the vertices of square A′B′C′D′ ?
(1 point)
10.Is figure T a reflection of figure S across the x -axis? Choose 1 for yes and 2 for no.(1 point)
11.Which of the following is an equivalent transformation to rotation of an object clockwise 90 degrees?(1 point)
12.given a point (−7, 4) on a geometric figure, what is the new point after rotating the figure 90 degrees counterclockwise?(1 point)
13.Given point A(2, 6) on the triangle, what are the new coordinates of the point after the triangle is rotated 180 degrees counterclockwise?
14.How would you describe the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II to show that the rectangles are congruent?(1 point)
1. The reflected line would have the same length as the original line, so the length of the reflected line would be 4 units.
2. To rotate the line segment 90° clockwise, we can swap the x and y coordinates of each endpoint and change the sign of the new y-coordinate. So the new endpoints would be (1, 5) and (4, 2).
3. After translating the side down 4 units and to the right 5 units, the length of the side would remain 10 units.
4. In the translated figure, the vertex H would be the same as the vertex of the original figure, since translating left 3 units does not change the x-coordinate.
5. After translating the triangle down 4 units and to the left 8 units, the length of side XY remains the same at 10 units. So the length of side X'Y' would also be 10 units.
6. After translating the triangle up 5 units and left 2 units, the coordinates of N' would be (-2, -1).
7. When a shape is reflected across the x-axis, the y-coordinate changes sign. So the coordinates for the point at the bottom of the heart in the reflected image would be (314, -712).
8. After reflecting the figure WXYZ across the y-axis, the point W will end up in Quadrant I.
9. When square ABCD is reflected across the x-axis and the y-axis, the new vertices would be A'(-A, -B), B'(-A, B), C'(A, B), D'(A, -B).
10. Without the given figures, it is not possible to determine if figure T is a reflection of figure S across the x-axis.
11. An equivalent transformation to rotating an object clockwise 90 degrees is rotating the object counterclockwise 270 degrees.
12. To rotate a point 90 degrees counterclockwise, we can swap the x and y coordinates of the point and change the sign of the new x-coordinate. So the new point would be (4, 7).
13. To rotate a point 180 degrees counterclockwise, we can change the sign of both the x and y coordinates of the point. So the new coordinates of point A would be (-2, -6).
14. The series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II and show that they are congruent is a reflection across the y-axis and a reflection across the x-axis.