6-17. On Graph Paper, Graph \[$\triangle ABC\$\] If Its Vertices Are \[$A(-2, 7), B(-5, 8)\$\], And \[$C(-3, 1)\$\].a. Reflect \[$\triangle ABC\$\] Across The \[$x\$\]-axis To Form \[$\triangle

Understanding the Problem

In this problem, we are given the vertices of a triangle {\triangle ABC$}$ and asked to graph it on graph paper. We are also required to reflect the triangle across the {x$}$-axis to form a new triangle {\triangle A'B'C'$}$.

Graphing the Original Triangle

To graph the original triangle {\triangle ABC$}$, we need to plot the vertices {A(-2, 7), B(-5, 8)$}$, and {C(-3, 1)$}$ on the graph paper.

• Vertex A: The x-coordinate of vertex A is -2, and the y-coordinate is 7. To plot this point, we move 2 units to the left of the origin (0, 0) and 7 units up.
• Vertex B: The x-coordinate of vertex B is -5, and the y-coordinate is 8. To plot this point, we move 5 units to the left of the origin (0, 0) and 8 units up.
• Vertex C: The x-coordinate of vertex C is -3, and the y-coordinate is 1. To plot this point, we move 3 units to the left of the origin (0, 0) and 1 unit down.

After plotting the vertices, we can draw the sides of the triangle to complete the graph.

Reflecting the Triangle Across the x-axis

To reflect the triangle across the x-axis, we need to change the sign of the y-coordinates of the vertices.

• Vertex A': The x-coordinate of vertex A' is still -2, but the y-coordinate is now -7 (since we reflected the original y-coordinate of 7 across the x-axis).
• Vertex B': The x-coordinate of vertex B' is still -5, but the y-coordinate is now -8 (since we reflected the original y-coordinate of 8 across the x-axis).
• Vertex C': The x-coordinate of vertex C' is still -3, but the y-coordinate is now -1 (since we reflected the original y-coordinate of 1 across the x-axis).

After changing the y-coordinates of the vertices, we can plot the new vertices and draw the sides of the reflected triangle {\triangle A'B'C'$}$.

Graphing the Reflected Triangle

To graph the reflected triangle {\triangle A'B'C'$}$, we plot the new vertices {A'(-2, -7), B'(-5, -8)$}$, and {C'(-3, -1)$}$ on the graph paper.

• Vertex A': The x-coordinate of vertex A' is -2, and the y-coordinate is -7. To plot this point, we move 2 units to the left of the origin (0, 0) and 7 units down.
• Vertex B': The x-coordinate of vertex B' is -5, and the y-coordinate is -8. To plot this point, we move 5 units to the left of the origin (0, 0) and 8 units down.
• Vertex C': The x-coordinate of vertex C' is -3, and the y-coordinate is -1. To plot this point, we move 3 units to the left of the origin (0, 0) and 1 unit down.

After plotting the vertices, we can draw the sides of the reflected triangle to complete the graph.

Conclusion

In this problem, we graphed the original triangle {\triangle ABC$}$ on graph paper and then reflected it across the x-axis to form a new triangle {\triangle A'B'C'$}$. We changed the y-coordinates of the vertices to reflect the triangle across the x-axis and plotted the new vertices to complete the graph.

Key Takeaways

• To graph a triangle on graph paper, we need to plot the vertices and draw the sides of the triangle.
• To reflect a triangle across the x-axis, we need to change the sign of the y-coordinates of the vertices.
• The reflected triangle will have the same x-coordinates as the original triangle, but the y-coordinates will be negated.

Practice Problems

• Graph the triangle {\triangle DEF$}$ with vertices {D(2, 3), E(4, 5)$}$, and {F(3, 2)$}$ on graph paper.
• Reflect the triangle {\triangle DEF$}$ across the x-axis to form a new triangle {\triangle D'E'F'$}$.
• Graph the reflected triangle {\triangle D'E'F'$}$ on graph paper.

Answer Key

• The graph of the triangle {\triangle DEF$}$ is a triangle with vertices {D(2, 3), E(4, 5)$}$, and {F(3, 2)$}$.
• The reflected triangle {\triangle D'E'F'$}$ has vertices {D'(2, -3), E'(4, -5)$}$, and {F'(3, -2)$}$.
• The graph of the reflected triangle {\triangle D'E'F'$}$ is a triangle with vertices {D'(2, -3), E'(4, -5)$}$, and {F'(3, -2)$}$.
  Q&A: Graphing and Reflecting Triangles on Graph Paper =====================================================

Frequently Asked Questions

Q: What is the first step in graphing a triangle on graph paper?

A: The first step in graphing a triangle on graph paper is to plot the vertices of the triangle. This involves moving the correct number of units to the left or right of the origin (0, 0) and up or down to plot each vertex.

Q: How do I reflect a triangle across the x-axis?

A: To reflect a triangle across the x-axis, you need to change the sign of the y-coordinates of the vertices. This means that if the original y-coordinate is positive, the reflected y-coordinate will be negative, and vice versa.

Q: What is the difference between the original triangle and the reflected triangle?

A: The original triangle and the reflected triangle have the same x-coordinates, but the y-coordinates of the reflected triangle are negated. This means that the reflected triangle is a mirror image of the original triangle across the x-axis.

Q: Can I reflect a triangle across the y-axis?

A: Yes, you can reflect a triangle across the y-axis. To do this, you need to change the sign of the x-coordinates of the vertices. This means that if the original x-coordinate is positive, the reflected x-coordinate will be negative, and vice versa.

Q: How do I graph a triangle with negative x-coordinates?

A: To graph a triangle with negative x-coordinates, you need to move the correct number of units to the left of the origin (0, 0). For example, if the x-coordinate is -2, you would move 2 units to the left of the origin.

Q: Can I graph a triangle with negative y-coordinates?

A: Yes, you can graph a triangle with negative y-coordinates. To do this, you need to move the correct number of units down from the origin (0, 0). For example, if the y-coordinate is -3, you would move 3 units down from the origin.

Q: What is the importance of graphing triangles on graph paper?

A: Graphing triangles on graph paper is an important skill in mathematics, as it helps you visualize and understand the properties of triangles. It also helps you develop your spatial reasoning and problem-solving skills.

Q: Can I use graph paper to graph other types of shapes?

A: Yes, you can use graph paper to graph other types of shapes, such as quadrilaterals, polygons, and circles. Graph paper is a versatile tool that can be used to graph a wide range of shapes and figures.

Q: How do I choose the correct scale for my graph?

A: To choose the correct scale for your graph, you need to consider the size of the shape you are graphing and the amount of space available on the graph paper. A good rule of thumb is to use a scale that is large enough to show the shape clearly, but not so large that it takes up too much space on the graph paper.

Q: Can I use graph paper to solve real-world problems?

A: Yes, you can use graph paper to solve real-world problems. Graph paper is a useful tool for visualizing and understanding complex problems, and it can be used to develop solutions to a wide range of problems.

Q: How do I use graph paper to graph a function?

A: To graph a function on graph paper, you need to plot the x and y values of the function on the graph paper. You can use a table of values or a graphing calculator to help you plot the function.

Q: Can I use graph paper to graph a system of equations?

A: Yes, you can use graph paper to graph a system of equations. To do this, you need to plot the x and y values of each equation on the graph paper and look for the points of intersection.

Q: How do I use graph paper to graph a parametric equation?

A: To graph a parametric equation on graph paper, you need to plot the x and y values of the equation as a function of the parameter. You can use a table of values or a graphing calculator to help you plot the equation.

Q: Can I use graph paper to graph a polar equation?

A: Yes, you can use graph paper to graph a polar equation. To do this, you need to plot the x and y values of the equation in polar coordinates. You can use a table of values or a graphing calculator to help you plot the equation.

Q: How do I use graph paper to graph a 3D shape?

A: To graph a 3D shape on graph paper, you need to use a 3D graph paper or a computer program that can graph 3D shapes. You can also use a graphing calculator or a computer program to help you graph the shape.

Q: Can I use graph paper to graph a fractal?

A: Yes, you can use graph paper to graph a fractal. To do this, you need to use a graphing calculator or a computer program that can graph fractals. You can also use a table of values or a graphing calculator to help you graph the fractal.

Q: How do I use graph paper to graph a mathematical model?

A: To graph a mathematical model on graph paper, you need to plot the x and y values of the model on the graph paper. You can use a table of values or a graphing calculator to help you plot the model.

Q: Can I use graph paper to graph a statistical distribution?

A: Yes, you can use graph paper to graph a statistical distribution. To do this, you need to plot the x and y values of the distribution on the graph paper. You can use a table of values or a graphing calculator to help you plot the distribution.

Q: How do I use graph paper to graph a probability distribution?

A: To graph a probability distribution on graph paper, you need to plot the x and y values of the distribution on the graph paper. You can use a table of values or a graphing calculator to help you plot the distribution.

Q: Can I use graph paper to graph a time series?

A: Yes, you can use graph paper to graph a time series. To do this, you need to plot the x and y values of the time series on the graph paper. You can use a table of values or a graphing calculator to help you plot the time series.

Q: How do I use graph paper to graph a financial model?

A: To graph a financial model on graph paper, you need to plot the x and y values of the model on the graph paper. You can use a table of values or a graphing calculator to help you plot the model.

Q: Can I use graph paper to graph a scientific model?

A: Yes, you can use graph paper to graph a scientific model. To do this, you need to plot the x and y values of the model on the graph paper. You can use a table of values or a graphing calculator to help you plot the model.

Q: How do I use graph paper to graph a mathematical proof?

A: To graph a mathematical proof on graph paper, you need to plot the x and y values of the proof on the graph paper. You can use a table of values or a graphing calculator to help you plot the proof.

Q: Can I use graph paper to graph a geometric shape?

A: Yes, you can use graph paper to graph a geometric shape. To do this, you need to plot the x and y values of the shape on the graph paper. You can use a table of values or a graphing calculator to help you plot the shape.

Q: How do I use graph paper to graph a fractal shape?

A: To graph a fractal shape on graph paper, you need to plot the x and y values of the shape on the graph paper. You can use a table of values or a graphing calculator to help you plot the shape.

Q: Can I use graph paper to graph a 3D fractal shape?

A: Yes, you can use graph paper to graph a 3D fractal shape. To do this, you need to use a 3D graph paper or a computer program that can graph 3D fractals. You can also use a graphing calculator or a computer program to help you graph the fractal.

Q: How do I use graph paper to graph a mathematical function?

A: To graph a mathematical function on graph paper, you need to plot the x and y values of the function on the graph paper. You can use a table of values or a graphing calculator to help you plot the function.

Q: Can I use graph paper to graph a parametric function?

A: Yes, you can use graph paper to graph a parametric function. To do this, you need to plot the x and y values of the function as a function of the parameter on the graph paper. You can use a table of values or a graphing calculator to help you plot the function.

Q: How do I use graph paper to graph a polar function?

A: To graph a polar function on graph paper, you need to plot the x and y values of the function in polar coordinates on the graph paper. You can use a table of values or a graphing calculator to help you plot the function.

Q: Can I use graph paper to graph a 3D function?

A: Yes, you can use graph paper to graph a 3D function. To do this, you need to use a 3D graph paper or a computer program that can graph 3D functions. You can also use a graphing calculator or a computer program to help you graph the