Finding Distance and Determining the 3rd Vertex of a Right Triangle!

DIRECTIONS

Read all problems carefully and show your work and thinking in your notebooks. Write down any questions you may have in your notebooks too. You may work with 1-2 partners, but responses must be submitted individually.

[size=100][size=150]There is a method we can use called the distance formula to find the distance between two points.
BUT - we can also use the Pythagorean Theorem!!

[b]This lesson will focus on using the Pythagorean Theorem in a coordinate grid. But for #1 you will verify the answer shown using the distance formula. [/b][/size][/size] — There is a method we can use called the distance formula to find the distance between two points. BUT - we can also use the Pythagorean Theorem!! **This lesson will focus on using the Pythagorean Theorem in a coordinate grid. But for #1 you will verify the answer shown using the distance formula.**

Example: If we want to find the distance between these two points - (2, 2) and (5, 6) - we need to find the length of (c)

Problem#0- Verify the answer is 5 units using the distance formula from do now!

Steps to solving the example above: 1. Draw a right triangle making the line between the two points the hypotenuse (c). 2. Find the length of the legs you just drew (a) and (b). 3. With all those values we now have a right triangle and can use the Pythagorean Theorem as follows:

We will use 3 for a (the bottom leg is 3 units), and 4 for b (the right leg is 4 units)

The distance between the points (2,2) and (5,6) is 5 units. **In your notebooks, verify the answer is 5 units using the distance formula. **

Problem #1: We want to find the distance between the two points below. But we need to start with forming a right triangle!

Click on the third box (line with one point on each end) and click segment. Start at (1,2) and place a new point on the coordinate plane. Connect it to (13, 7). This should make a right triangle.

1. What is your new point? We call this point the third vertex of the right triangle. (If you did not make a right triangle, try another point. There is more than 1 correct answer) 2. What do you notice about the x-coordinate and y-coordinate of the third vertex of the right triangle? (Hint: Compare it to (1,2) and (13,7). Do you notice anything?)

Problem #1 continued: Using the third vertex to find the distance between (1,2) and (13,7).

Plot the third vertex you found before. Answer the question below.

1. What is the distance between (1,2) and (13,7)? Include units. Explain your thinking in 1-2 sentences.

Problem #2: Finding the distance between (1,3) and (16,11)

Problem #2: Find the distance between (1,3) and (16,11) by first finding the third vertex and then applying the Pythagorean theorem.

1. What is the distance between (1,2) and (13,7)? Include units. Explain your thinking in 1-2 sentences.

Group A: Find and plot the third vertex

Plot a third vertex that makes this triangle a right triangle.

1. What are the coordinates of the third vertex? 2. Compare with your partner. a. Did you find the same third vertex? YES: -Explain how you both know it is correct in at least 2 sentences. -Find another point that could be the third vertex of this right triangle. -Explain how you know this other point is correct in at least 2 sentences. NO: -Explain your steps to each other and write down both steps in your notebook. -Check each other's point by comparing the x and y coordinates to (2, -2) and (8,4). Write at least two sentences here about what you notice. -Decide if you agree or disagree with your partner's third vertex? Write at least 2 sentences why you agree or why you disagree.

Group B: Pick a third vertex and find the distance.

1. Identify the coordinates of the third vertex. 2. Find the distance from (1,-1) and (8,5). Include units. 3. Suppose you picked a different vertex that still makes the triangle a right triangle. -Predict if the distance from (1,-1) and (8,5) will stay the same or change? -Explain why or why not using at least 3 sentences.

Group C: Find the distance between (-3,1) and (6,4)

1. Find two different points that could be the third vertex of this right triangle. Write the ordered pairs below and plot them on the graph. 2. For each vertex, explain in 2 sentences why this is a third vertex of this right triangle. 3. Pick only 1 vertex that you found and use it find the distance between (-3, 1) and (6,4). Include units. 4. Verify your answer by picking the other vertex and using it to find the distance between (-3, 1) and (6,4). Include units.