Find the coordinates of the image of point R(3, –5) rotated 180° about the origin.
A. (–3, 5)
B. (–5, –3)
C. (5, 3)
D. (3, –5)
When a point is rotated 180° about the origin, its x-coordinate and y-coordinate are both multiplied by -1. Therefore, the image of point R(3, -5) would be (-3, 5). Therefore, the answer is A. (-3, 5).
An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry? Explain.
Yes, the Ferris wheel has rotational symmetry.
Rotational symmetry occurs when an object can be rotated around a center point by an angle less than 360 degrees and still look the same as it did before the rotation.
In the case of an 8-car Ferris wheel shaped like a regular octagon, the wheel can be rotated by 45 degrees (360/8) around its center point and still look the same. Each car will be in the same position in relation to the others, the angles between the cars will be the same, and the wheel will have the same overall shape.
Therefore, the Ferris wheel has rotational symmetry with a rotational angle of 45 degrees.
Triangle STU below is translated right 2 units and 3 units down. What are the coordinates of the vertices of the image?
A coordinate grid with triangle S T U drawn on the grid is shown.The x-axis is between negative 12 and 4 with interval marks representing one unit, and the y-axis is between negative 4 and 14 with interval marks representing one unit. Triangle S T U is drawn in red with vertex S at left-parenthesis negative 6 comma 10 right-parenthesis, vertex T at left-parenthesis negative 9 comma 3 right-parenthesis, and vertex U at left-parenthesis negative 3 comma 3 right-parenthesis.
A. S’(−9, 12), T’(−12, 5), U’(−6, 5)
B. S’(−4, 7), T’(−7, 0), U’(−1, 0)
C. S’(−8, 13), T’(−11, 6), U’(−5, 6
D. S’(−4, 10), T’(−7, 3), U’(−1, 3)
To translate a point to the right 2 units and down 3 units, we subtract 2 from the x-coordinate and subtract 3 from the y-coordinate.
Applying this translation to each vertex of triangle STU, we get:
- Vertex S: (-6, 10) becomes S' = (-6 - 2, 10 - 3) = (-8, 7)
- Vertex T: (-9, 3) becomes T' = (-9 - 2, 3 - 3) = (-11, 0)
- Vertex U: (-3, 3) becomes U' = (-3 - 2, 3 - 3) = (-5, 0)
Therefore, the coordinates of the vertices of the image are S’(-8, 7), T’(-11, 0), and U’(-5, 0).
The answer is C. S’(-8, 13), T’(-11, 6), U’(-5, 6) is not correct because the y-coordinate of the original triangle is not 13 or 6, and the translation moves the triangle down, not up. S’(-4, 10), T’(-7, 3), U’(-1, 3) is not correct because the x-coordinates of the original triangle are not 4, 7, or 1.
Choose the graph that represents the equation y = x – 2.
A. graph
B. graph
C. graph
A. graph.
The graph in option A passes through the point (0, -2) and has a slope of 1 (meaning that as x increases by 1 unit, y increases by 1 unit). This matches the equation y = x - 2.
Option B has a slope of 2, which does not match the slope of 1 in the equation y = x - 2.
Option C has a slope of -1, which also does not match the slope of 1 in the equation y = x - 2.
Which graph shows the image of the triangle below after it is reflected over the x-axis?
graphThe x-axis is between negative 4 and 4 with interval marks representing one unit, and the y-axis is between negative 5 and 5 with interval marks representing one unit. A triangle is drawn in red with vertices at left-parenthesis 1 comma 1 right-parenthesis, left-parenthesis 3 comma 1 right-parenthesis, and left-parenthesis 1 comma 3 right-parenthesis.
A. graph
B. graph
C. graph
D. graph
The vertices of the original triangle are (1, 1), (3, 1), and (1, 3).
When a point is reflected over the x-axis, its y-coordinate changes sign. Therefore, the coordinates of the reflected vertices would be:
- (1, 1) reflects to (1, -1)
- (3, 1) reflects to (3, -1)
- (1, 3) reflects to (1, -3)
The graph that shows the image of the triangle after it is reflected over the x-axis is option B.
In option B, the original triangle is drawn in red, and the reflected image is drawn in blue. The coordinates of the reflected vertices match the coordinates we found above, and the image appears to be a mirror reflection of the original triangle over the x-axis.
Option A is the original triangle without any reflection. Option C shows a translation of the original triangle but no reflection. Option D shows a reflection over the y-axis, not the x-axis.
Determine which ordered pair is a solution of y = x2–2.
(5, 21), (–5, 24), (–1, –1), (–2, 6)
A. (–2, 6)
B. (5, 21)
C. (–1, –1)
D. (–5, 24)