1. 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.
2. 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.
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1. After reflecting triangle ABC over the y-axis, the coordinates of the reflected triangle are as follows:
Vertex A' is at the point (-1, 3)
Vertex B' is at the point (-4, 5)
Vertex C' is at the point (-3, 1)
In this reflection, the x-coordinates of the original triangle's vertices change sign (positive becomes negative, negative becomes positive), while the y-coordinates remain the same.
2. After translating triangle ABC 1 unit right and 2 units down, the coordinates of the translated triangle are as follows:
Vertex A' is at the point (2, 1)
Vertex B' is at the point (5, 3)
Vertex C' is at the point (4, -1)
The rule for this translation can be written as:
(Triangle ABC) -> (Triangle A'B'C') where:
A'(x, y) = A(x + 1, y - 2)
B'(x, y) = B(x + 1, y - 2)
C'(x, y) = C(x + 1, y - 2)
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1. When the triangle is reflected over the y-axis, the x-coordinates of the original triangle's vertices change signs, while the y-coordinates remain the same.
The coordinates of the reflected triangle are:
- Vertex A: (-1, 3)
- Vertex B: (-4, 5)
- Vertex C: (-3, 1)
2. When the triangle is translated 1 unit right and 2 units down, each coordinate of the original triangle's vertices is modified as follows:
- To translate right, add 1 to the x-coordinate.
- To translate down, subtract 2 from the y-coordinate.
The coordinates of the translated triangle are:
- Vertex A: (2, 1)
- Vertex B: (5, 3)
- Vertex C: (4, -1)
The translation rule can be written using arrow notation as follows:
Starting position -> 1 unit right, 2 units down
I'm sorry to hear that you haven't been feeling well and your grades have been dropping. I'm here to help you understand these concepts. Let's go through each question step by step.
1. Reflection over the y-axis:
To find the coordinates of the reflected triangle, we need to reflect each vertex of the original triangle over the y-axis.
Looking at the original triangle, we have:
Vertex A: (1, 3)
Vertex B: (4, 5)
Vertex C: (3, 1)
To reflect a point over the y-axis, we need to reverse the sign of the x-coordinate and keep the y-coordinate the same.
Applying this to each vertex of the original triangle, we get:
Vertex A' (reflected A): (-1, 3)
Vertex B' (reflected B): (-4, 5)
Vertex C' (reflected C): (-3, 1)
Therefore, the coordinates of the reflected triangle are:
A' (-1, 3)
B' (-4, 5)
C' (-3, 1)
To describe what happens to the x-coordinates and y-coordinates of the original triangle's vertices as a result of this reflection:
- The x-coordinates change signs (positive to negative or negative to positive) due to reflection over the y-axis.
- The y-coordinates remain the same.
2. Translation:
To find the coordinates of the translated triangle, we need to shift each vertex of the original triangle according to the given directions.
Looking at the original triangle, we have:
Vertex A: (1, 3)
Vertex B: (4, 5)
Vertex C: (3, 1)
The translation rule states that we move the triangle a certain number of units to the right (positive) or left (negative) and a certain number of units up (positive) or down (negative).
In this case, the triangle is translated 1 unit to the right (x-coordinate increases) and 2 units down (y-coordinate decreases).
Applying this to each vertex of the original triangle, we get:
Vertex A' (translated A): (1 + 1, 3 - 2) = (2, 1)
Vertex B' (translated B): (4 + 1, 5 - 2) = (5, 3)
Vertex C' (translated C): (3 + 1, 1 - 2) = (4, -1)
Therefore, the coordinates of the translated triangle are:
A' (2, 1)
B' (5, 3)
C' (4, -1)
To write a rule for this translation using arrow notation:
(x, y) -> (x + 1, y - 2)
I hope this explanation helps you understand and solve these questions. If you have any further questions, feel free to ask. Don't worry, I'm here to assist you.