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'?
__ units
The translation down 4 units and to the left 8 units means that every point in the original triangle is moved 4 units down and 8 units to the left.
Since side XY is 10 units, the length of side X'Y' will also be 10 units.
Therefore, the length of side X'Y' is 10 units.
Triangle MNO is translated up 5 units and left 2 units. Point N is located at (0, -6). What are the coordinates of N'?
A. (-2, -1)
B. (2, -1)
C. (-2, -11)
D. (5, -8)
Since the triangle is translated up 5 units and left 2 units, the x-coordinate of N' will be 0 - 2 = -2 and the y-coordinate will be -6 + 5 = -1.
Therefore, the coordinates of N' are (-2, -1).
Thus, the correct answer is A. (-2, -1).
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 (3 1/4, 7 1/2), what are the coordinates for the point at the bottom of the heart in the reflected image?
When a shape is reflected across the x-axis, the y-coordinates of all the points are negated, while the x-coordinates remain the same.
In this case, since the original point at the bottom of the heart is at (3 1/4, 7 1/2), the x-coordinate remains 3 1/4, and the y-coordinate becomes -7 1/2.
Therefore, the coordinates for the point at the bottom of the heart in the reflected image are (3 1/4, -7 1/2).
Coordinates: W (-2, 1), X (-4, -3), Y (5, 2), Z (6, 6)
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?
A. Point X
B. Point Z
C. Point Y
D. Point W
When a figure is reflected across the y-axis, the x-coordinates of all the points are negated, while the y-coordinates remain the same.
Let's determine the new coordinates of each point after reflecting across the y-axis:
- Point W: (-2, 1) -> (-(-2), 1) -> (2, 1)
- Point X: (-4, -3) -> (-(-4), -3) -> (4, -3)
- Point Y: (5, 2) -> (-5, 2)
- Point Z: (6, 6) -> (-6, 6)
Out of these new coordinates, only Point Y: (-5, 2) will end up in Quadrant I.
Therefore, the correct answer is C. Point Y.
Coordinates A(3,-4), B(7,-4), C(7,-8), D(3,-8)
Reflect square ABCD with respect to the x-axis and the y-axis. What are the vertices of square A'B'C'D'?
A. Square A'B'C'D' has vertices A'(-3,-4), B'(-7,-4), C'(-7-8), and D'(-3,-8)
B. Square A'B'C'D' has vertices A'(3,4), B'(7,4), C'(7,8), and D'(3,8)
C. Square A'B'C'D' has vertices A'(-3,4), B'(-7,4), and C'(-7,8)
D. Square A'B'C'D' has vertices A' (-3,4), B'(-7,4), C'(-7,8), D'(-3,8)
When a figure is reflected across the x-axis, the y-coordinates of all the points are negated, while the x-coordinates remain the same. When a figure is reflected across the y-axis, the x-coordinates of all the points are negated, while the y-coordinates remain the same.
Let's determine the new coordinates of each point after reflecting across the x-axis and y-axis:
- Reflecting across the x-axis:
Coordinates A(3,-4) -> (3,-(-4)) -> (3,4)
Coordinates B(7,-4) -> (7,-(-4)) -> (7,4)
Coordinates C(7,-8) -> (7,-(-8)) -> (7,8)
Coordinates D(3,-8) -> (3,-(-8)) -> (3,8)
- Reflecting across the y-axis:
Coordinates A'(3,4) -> (-3,4)
Coordinates B'(7,4) -> (-7,4)
Coordinates C'(7,8) -> (-7,8)
Coordinates D'(3,8) -> (-3,8)
Therefore, the vertices of square A'B'C'D' are A'(-3,4), B'(-7,4), C'(-7,8), and D'(-3,8).
The correct answer is D. Square A'(-3,4), B'(-7,4), C'(-7,8), D'(-3,8).
Which of the following is an equivalent transformation to rotation of an object clockwise 90 degrees?
A. rotation about the origin of 90 degrees counterclockwise
B. rotation about the origin of 270 degrees clockwise
C. rotation about the origin of 180 degrees counterclockwise
D. rotation about the origin of 270 degrees counterclockwise