Which translation rule describes the translation that is 6 units to the right and 5 units down?
(1 point)
Responses
(x, y) → (x + 6, y – 5)
( x, y ) → ( x + 6, y – 5)
(x, y) → (x – 6, y – 5)
( x, y ) → ( x – 6, y – 5)
(x, y) → (x + 6, y + 5)
( x, y ) → ( x + 6, y + 5)
(x, y) → (x – 6, y + 5)
(x, y) → (x + 6, y – 5)
use step by step
To describe a translation that is 6 units to the right and 5 units down, follow these steps:
1. Start with the original point (x, y).
2. Move the x-coordinate 6 units to the right by adding 6 to x: x + 6.
3. Move the y-coordinate 5 units down by subtracting 5 from y: y - 5.
4. Write the translation rule in the form (x, y) → (x + 6, y - 5).
Therefore, the correct translation rule is (x, y) → (x + 6, y - 5).
If point P left parenthesis 4 comma 11 right parenthesis is reflected across the line y = 3, what are the coordinates of its reflection image?
(1 point)
Responses
left parenthesis 2 comma 11 right parenthesis
Image with alt text: left parenthesis 2 comma 11 right parenthesis
left parenthesis 11 comma 4 right parenthesis
Image with alt text: left parenthesis 11 comma 4 right parenthesis
left parenthesis 4 comma negative 11 right parenthesis
Image with alt text: left parenthesis 4 comma negative 11 right parenthesis
left parenthesis 4 comma negative 5 right parenthesis
To reflect a point across the line y = 3, we need to keep the x-coordinate the same and change the sign of the y-coordinate.
Given point P (4, 11), when reflected across the line y = 3, the y-coordinate will be negated.
So, the reflected image of point P will have the coordinates:
(4, -11)
Therefore, the correct coordinates of the reflection image are (4, -11).
The vertices of a triangle are P(–4, 1), Q(–2, –8), and R(8, –1). What are the vertices of the image reflected across the x-axis?
(1 point)
Responses
P'(–4, –1), Q'(–2, 8), and R'(8, 1)
P' (–4, –1), Q' (–2, 8), and R' (8, 1)
P'(4, –1), Q'(2, 8), and R'(–8, 1)
P' (4, –1), Q' (2, 8), and R' (–8, 1)
P'(4, 1), Q'(2, –8), and R'(–8, –1)
P' (4, 1), Q' (2, –8), and R' (–8, –1)
P'(–4, 1), Q'(–2, –8), and R'(8, –1)
To reflect a point across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
Given the vertices of the triangle: P(-4, 1), Q(-2, -8), and R(8, -1), when reflected across the x-axis, the y-coordinate of each vertex will be negated.
So, the coordinates of the reflected vertices will be:
P' (-4, -1), Q' (-2, 8), and R' (8, 1).
Therefore, the correct vertices of the image reflected across the x-axis are P' (-4, -1), Q' (-2, 8), and R' (8, 1).
Which graph shows a triangle and its reflection image across the y-axis?
(1 point)
Responses
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis.
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The correct graph that shows a triangle and its reflection image across the y-axis is:
Two right triangles are shown on the coordinate plane. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
Therefore, the correct response is:
Two right triangles are shown on the coordinate plane. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
The hexagon GIKMPR is regular. The dashed line segments form 30° angles.
Hexagon GIKMPR is shown.A hexagon is shown. A point in the middle of the hexagon is labeled O. There are points labeled at each vertex and at the midpoints of each side of the hexagon. Starting at the top of the image, the midpoint of the side is labeled F. Moving clockwise, the points are labeled G, H, I, J, K, L, M, N, N, P Q, and R. There are 6 dotted lines drawn through the hexagon and through point O. One connects midpoints F and L. One connects vertices G and M. One connects midpoints H and N. One connects vertices I and P. One connects midpoints J and Q. One connects vertices K and R.
What is the image of ON after a rotation of 180°?
(1 point)
Responses
ON
ON
OH
OH
OJ
OJ
OL