1. Which of the following tables of values is correct for the equation y equals negative 3 x squared?
2. Find the horizontal change and the vertical change for the translation
3. 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?
4. How many lines of symmetry does the figure below have? If there are no lines of symmetry, write none.
5. 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.
6. The point C(x, y) is reflected over the x-axis. Write a translation rule to describe the original point and its reflection.
7. 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.
8. 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.
sure*
1. To determine the correct table of values for the equation y = -3x^2, you can substitute different values of x into the equation and calculate the corresponding y-values. Here's how you can do it:
- Pick a range of values for x, such as -2, -1, 0, 1, and 2.
- Substitute each value of x into the equation and calculate the corresponding y-values.
- For example, when x = -2, y = -3(-2)^2 = -12. When x = -1, y = -3(-1)^2 = -3. And so on.
- Record the x and y values in a table format and compare them to the given tables of values. The correct table will have the corresponding values that satisfy the equation y = -3x^2.
2. To find the horizontal change and vertical change for a translation, follow these steps:
- Identify the original point and its coordinates.
- Identify the image point after translation and its coordinates.
- The horizontal change is the difference between the x-coordinates of the original and image points.
- The vertical change is the difference between the y-coordinates of the original and image points.
3. a. To write the rule for the translation of point C(3, -1) to the left 4 units and up 1 unit, you can apply the following steps:
- To move left 4 units, subtract 4 from the x-coordinate.
- To move up 1 unit, add 1 to the y-coordinate.
Combining both steps, the rule for this translation is (x - 4, y + 1).
b. To find the coordinates of the image point, apply the translation rule to the original point C(3, -1):
- Subtract 4 from the x-coordinate: 3 - 4 = -1.
- Add 1 to the y-coordinate: -1 + 1 = 0.
Therefore, the coordinates of the image point are (-1, 0).
4. To determine the number of lines of symmetry in a figure, you need to analyze its properties. Look for any lines that can divide the figure into two identical halves. If you find any lines that satisfy this condition, count them as lines of symmetry. If you don't find any such lines, the answer is "none."
5. The original triangle ΔABC has vertices A(2, -5), B(-3, 5), and C(3, -3). To describe the original triangle and its reflection over the x-axis using arrow notation, follow these steps:
- Draw arrows from the original vertices to their corresponding images.
- For the reflection over the x-axis, the y-coordinate of each point will change sign (positive becomes negative, and negative becomes positive). Keep the x-coordinate the same.
Using arrow notation, the original triangle ΔABC would be written as A(2, -5) --> B(-3, 5) --> C(3, -3), and its reflection over the x-axis would be A(2, 5) --> B(-3, -5) --> C(3, 3).
6. To write a translation rule describing the original point C(x, y) and its reflection over the x-axis, follow these steps:
- For the reflection over the x-axis, the x-coordinate of the point remains the same, but the y-coordinate changes sign (positive becomes negative, and negative becomes positive).
- So the translation rule for the reflection over the x-axis is (x, -y).
7. The reflected triangle ABC has the same vertices as the original triangle, but their coordinates change due to the reflection over the y-axis. To find the coordinates of the reflected triangle, follow these steps:
- Change the sign of the x-coordinate for each vertex of the original triangle.
- Leave the y-coordinate unchanged.
The coordinates of the reflected triangle ABC are: A(-1, 3), B(-4, 5), C(-3, 1).
The x-coordinates of the original triangle's vertices change sign, while the y-coordinates remain the same. This means that each vertex is reflected across the y-axis, resulting in a mirror image of the original triangle.
8. The original triangle ABC has vertices A(1, 3), B(4, 5), and C(3, 1). To translate the triangle 1 unit right and 2 units down, follow these steps:
- Add 1 to the x-coordinate of each vertex to move the triangle 1 unit to the right.
- Subtract 2 from the y-coordinate of each vertex to move the triangle 2 units down.
The coordinates of the translated triangle ABC are: A(2, 1), B(5, 3), C(4, -1).
Using arrow notation, the translation rule for this transformation would be: A(1, 3) --> A(2, 1), B(4, 5) --> B(5, 3), C(3, 1) --> C(4, -1).
#1 no table
the rest, what are your answers?
show your work so we can tell what's happening.