Question

Graph a Triangle Independently
Throughout this module, you have identified and constructed different types of triangles. Now you will graph one.
You are going to plot three random points on the coordinate plane and draw segments between them, creating a triangle. You will then use algebra to draw the medians and classify the type of triangle graphed.

Answer 1

Here is the complete question:
Graph a Triangle Independently
Throughout this module, you have identified and constructed different types of triangles. Now you will graph one.
You are going to plot three random points on the coordinate plane and draw segments between them, creating a triangle. You will then use algebra to draw the medians and classify the type of triangle graphed.
Part One:
1. On graph paper or using a drawing program, such as GeoGebra, plot three points on the coordinate plane.
2. Label each point with a letter and its corresponding ordered pair.
3. Draw segments between the points to form a triangle.
4. Use the midpoint formula to find and plot the midpoint of each segment. You must show your work.
5. Draw the three medians of the triangle.
6. Draw the centroid – the point of intersection between all three medians.
7. Estimate the ordered pair of the centroid.
You may use any drawing program you wish, but a GeoGebra window is shown below for your convenience. Follow thedirections to draw your triangle and save it to your computer so you may send it to your instructor.
Part Two:
1. Show your graph to three different individuals. They may be family, friends, or classmates.
2. Ask each person whether they think your triangle is scalene, isosceles, or equilateral. Remember, the people you ask may not know what these terms mean, so you might have to provide them with a definition.
3. Use the distance formula to find the length of each side of the triangle.
4. Classify your triangle as scalene, isosceles, or equilateral. Show work or provide an explanation to justify this classification.



Reflection:
After completing both parts of the activity, reflect upon your results. Answer the following questions using complete sentences.
1. How many medians are needed to find the centroid? Why?
2. How did the distance formula help you determine if the triangle is scalene, isosceles, or equilateral?
What do you turn in:
Submit the following to your instructor:
• a graph of your triangle with seven points labeled by letter and ordered pair (three vertices, three midpoints, one centroid) and medians.
• your algebraic work to find the ordered pairs of each midpoint.
• the names of those individuals to whom you showed your graph with their corresponding responses.
• your algebraic work to find the length of each side of the triangle.
• the identification of your triangle as scalene, isosceles, or equilateral.
• answers to the reflection questions.