2nd Quarter - Project 2

You will work individually or in pairs for this activity.

The activity can be found on page 280 of your books. For that you will create any necessary diagrams at geogebra in order to enhance your explanations. You will copy the questions and give complete answers.

Deadline for this activity is November 13th (G day).

Mrs. Saatkamp

2nd Quarter - Project 1

You will work with book pages 240 and 241.

Complete those pages on a word document, making sure to turn in your modeling activities.

You are allowed to work individually or in pairs (of your choice).

Deadline is October 30th (C Day)

Challenge 2 - Investigating Multiple Transformations

For the following graphs solve questions 1 to 3:

1) Draw the following graphs on geogebra. Keep the same coordinates as well as their labels.

2) The points with prime notation (A'', B'', ...) represent the image of more than one transformation of the preimage. Each prime symbol represents one transformation. Show the steps that you can use to get from the preimage to the final image.

3) Graph the intermediate image and describe each step to get from the preimage to the intermediate image and finally to the final image.

Trapezoid E''F''G''H'' resulted after two transformations. Use this to answer questions 4 and 5:

4) Make a conjecture about the coordinates of the vertices of trapezoid E'F'G'H'. Explain your conjecture, by explaining the transformation.

5) Is this the only possible solution for the coordinates of E'F'G'H'? Explain.

Challenge 1 - Center of Mass

The center of mass, also called the center of gravity, is the point where the weight of an object is focused. It is the point of balance of an object.

In a triangle, the center of mass is called the centroid. The centroid is found by drawing the three medians of the triangle. A median of a triangle is a segment that joins a vertex and the midpoint of the side opposite the vertex. The centroid of the triangle is the intersection point of the medians.

For this assignment you will need to use geogebra for your constructions.

Questions:

1) At geogebra, construct a triangle with vertices J, K, and L. Draw and label the three midpoints A, B and C. Draw the three medians.

2) Through geogebra, find the tool to calculate the length of a segment. Find the length of each median. then find the distance from each vertex to the centroid. Round your answers to the nearest tenth of a centimeter.

3) Use your results from exercise 2 to make a conjecture about how the distance from a vertex to the centroid is related to the distance from that vertex to the midpoint of the opposite side.

4) Points W, P , and Y are the midpoints of EF, FG, and GE, respectively. Use the triangle to verify the conjecture that you made in exercise 3.