Find the horizontal change and the vertical change for the translation
P(4, –4) right arrow (–4, 7).
A. right 8; up 11
B. left 8; down 11
C. right 8; down 11
D. left 8; up 11
The horizontal change is found by subtracting the x-coordinates: -4 - 4 = -8. The vertical change is found by subtracting the y-coordinates: 7 - (-4) = 11.
Therefore, the answer is:
C. right 8; down 11
The point C(3, –1) is translated to the left 4 units and up 1 unit.
a. Write the rule for this translation.
b. What are the coordinates of the image point?
A. (x, y) right arrow (x + 4, y +1); (7, –2)
B. (x, y) right arrow (x – 4, y – 1); (–1, 0)
C. (x, y) right arrow (x + 4, y – 1); (7, 0)
D. (x, y) right arrow (x – 4, y + 1); (–1, 0)
a. The rule for this translation is (x, y) -> (x - 4, y + 1).
b. Applying this rule to point C(3, -1), we get:
(3, -1) -> (3 - 4, -1 + 1) -> (-1, 0)
Therefore, the coordinates of the image point are (-1, 0).
The answer is:
B. (x, y) right arrow (x – 4, y – 1); (–1, 0)
The vertices of ΔABC are A(2, –5), B(–3, 5), and C(3, –3). The triangle is reflected over the x-axis. Use arrow notation to describe the original triangle and its reflection.
A. A(2, –5), B(–3, 5), C(3, –3) right arrow(2, –5), (–3, 5), (3, –3)
B. A(2, –5), B(–3, 5), C(3, –3) right arrow(–2, 5), (3, –5), (–3, 3)
C. A(2, –5), B(–3, 5), C(3, –3) right arrow(–2, –5), (3, 5), (–3, –3)
D. A(2, –5), B(–3, 5), C(3, –3) right arrow(2, 5), (–3, –5), (3, 3)
To reflect a point over the x-axis, we keep the x-coordinate the same and negate the y-coordinate.
Therefore, the reflected vertices of triangle ABC would be:
A(2, -(-5)) -> A(2, 5)
B(-3, -(5)) -> B(-3, -5)
C(3, -(-3)) -> C(3, 3)
Using arrow notation, the original triangle and its reflection can be described as:
A. A(2, –5), B(–3, 5), C(3, –3) right arrow (2, –5), (–3, 5), (3, –3)
This is not the correct answer, as the reflection over the x-axis would change the signs of the y-coordinates.
B. A(2, –5), B(–3, 5), C(3, –3) right arrow (–2, 5), (3, –5), (–3, 3)
This is also not the correct answer, as the x-coordinates of the vertices have been negated, but not the y-coordinates.
C. A(2, –5), B(–3, 5), C(3, –3) right arrow (–2, –5), (3, -5), (–3, –3)
This is not the correct answer, as only the y-coordinates have been negated, not reflected over the x-axis.
D. A(2, –5), B(–3, 5), C(3, –3) right arrow (2, 5), (–3, –5), (3, 3)
This is the correct answer, as both the x-coordinates and y-coordinates have been properly reflected over the x-axis.
Therefore, the answer is:
D. A(2, –5), B(–3, 5), C(3, –3) right arrow (2, 5), (–3, –5), (3, 3)
The point C(x, y) is reflected over the x-axis. Write a translation rule to describe the original point and its reflection.
A. (x, y) right arrow (x, 2y)
B. (x, y) right arrow (–x, y)
C. (x, y) right arrow (–x, –y)
D. (x, y) right arrow (x, –y)
To reflect a point over the x-axis, we keep the x-coordinate the same and negate the y-coordinate.
Therefore, the reflection of point C(x, y) would be (x, -y).
Using arrow notation, the translation rule to describe the original point and its reflection can be written as:
D. (x, y) right arrow (x, -y)
This rule means that to go from the original point (x, y) to its reflection, we keep the x-coordinate the same and change the sign of the y-coordinate.
Therefore, the answer is:
D. (x, y) right arrow (x, -y)
Triangle ABC is shown on the graph below.
Triangle ABC is shown on a graph. Vertex A is at the point left parenthesis 1 comma 3 right parenthesis. Vertex B is at the point left parenthesis 4 comma 5 right parenthesis. Vertex C is at the point left parenthesis 3 comma 1 right parenthesis.
Triangle ABC is reflected over the y-axis. What are the coordinates of the reflected triangle?
Describe in words what happens to the x-coordinates and y-coordinates of the original triangle’s vertices as a result of this reflection.
The original triangle ABC has vertices at A(1, 3), B(4, 5), and C(3, 1).
To reflect the triangle over the y-axis, we keep the y-coordinate the same and negate the x-coordinate. Therefore, the coordinates of the reflected triangle would be:
A(-1, 3), B(-4, 5), and C(-3, 1).
In other words, the x-coordinates of the original triangle's vertices have been negated while the y-coordinates remain the same in the reflected triangle.
The reflection across the y-axis is a transformation that mirrors points across the y-axis. The x-coordinate of a point is negated and the y-coordinate remains the same. As a result of this transformation, the object appears as a mirror image of itself across the y-axis.
Triangle ABC is shown on the graph below.
Triangle ABC is shown on a graph. Vertex A is at the point left parenthesis 1 comma 3 right parenthesis. Vertex B is at the point left parenthesis 4 comma 5 right parenthesis. Vertex C is at the point left parenthesis 3 comma 1 right parenthesis.
Triangle ABC is translated 1 unit right and 2 units down. What are the coordinates of the translated triangle?
Use arrow notation to write a rule for this translation.