[b]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. [br][/b]
[size=100][size=150]There is a method we can use called the distance formula to find the distance between two points. [br]BUT - we can also use the Pythagorean Theorem!! [br][br][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]
[br][u][i][b]Steps to solving the example above:[/b][/i][/u][br]1. Draw a right triangle making the line between the two[br] points the hypotenuse (c).[br] 2. Find the length of the legs you just drew (a) and (b). [br] 3. With all those values we now have a right triangle and[br] can use the Pythagorean Theorem as follows:[br][math]a^2+b^2=c^2[br][/math][br][math]3^2+4^2=c^2[/math] We will use 3 for a (the bottom leg is 3 units), and 4 for b (the right leg is 4 units)[br][math]9+16=c^2[/math][br][math]25=c^2[/math][br][math]\sqrt{25}=\sqrt{c^2}[/math][br][math]5=c[/math] The distance between the points (2,2) and (5,6) is 5 units.[b] [br][br][u]**In your notebooks, verify the answer is 5 units using the distance formula. **[br][/u][/b][br][br]
[b]1[/b]. What is your new point? We call this point the[b] third vertex[/b] of the right triangle. (If you did not make a right triangle, try another point. There is more than 1 correct answer)[br][br][br][b]2[/b]. What do you notice about the [i]x-coordinate[/i] and [i]y-coordinate[/i] of the [b]third vertex[/b] of the right triangle? (Hint: Compare it to (1,2) and (13,7). Do you notice anything?)[br][br][br]
1. What is the [b]distance[/b] between (1,2) and (13,7)? Include [b]units[/b]. Explain your thinking in 1-2 sentences.
1. What is the [b]distance [/b]between (1,2) and (13,7)? Include [b]units[/b]. Explain your thinking in 1-2 sentences.
[b]1[/b]. What are the [b]coordinates[/b] of the third vertex?[br][br][br][b]2. Compare[/b] with your partner. [br] a. Did you find the same third vertex? [br] [b][u] YES:[/u][/b][br] -[b]E[/b][b]xplain [/b]how you both know it is correct in [b]at least 2 sentences[/b].[br] -[b]Find another point [/b]that could be the third vertex of this right triangle. [br] -[b]Explain[/b] how you know this other point is correct in [b]at least 2 [br] sentences.[/b][br] [br] [br] [b][u]NO: [br][/u][/b] -[b]Explain [/b]your steps to each other and [b]write[/b] down both steps in your[br] notebook. [br] -[b]Check[/b] each other's point by comparing the x and y coordinates to [br] (2, -2) and (8,4). Write [b]at least two sentences[/b] here about what you [br] notice. [br] -[b]Decide[/b] if you agree or disagree with your partner's third vertex? Write [br] [b]at least 2 sentences[/b] why you agree or why you disagree. [br]
[b]1.[/b] Identify the [b]coordinates[/b] of the third vertex.[br][br][br][b]2.[/b] Find the [b]distance[/b] from (1,-1) and (8,5). Include [b]units[/b].[br][br][br][b]3. [/b]Suppose you picked a [b]different vertex[/b] that still makes the triangle a right[br] triangle.[br][b] -Predict [/b]if the distance from (1,-1) and (8,5) will stay the same or change? [br][b] -Explain [/b]why or why not using [b]at least 3 sentences. [/b][br]
[b]1.[/b] Find [b]two different [/b]points that could be the third vertex of this right triangle. Write the ordered pairs below and plot them on the graph. [br][br][b]2.[/b] For [b]each[/b] vertex, [b]explain[/b] [b]in 2 sentences[/b] why this is a third vertex of this right [br] triangle.[br][br][br][b]3.[/b] [b]Pick[/b] only 1 vertex that you found and use it find the [b]distance[/b] between (-3, 1) and[br] (6,4). Include [b]units[/b].[br][br][b]4.[/b] [b]Verify [/b]your answer by picking the other vertex and using it to find the [b]distance[br] [/b]between (-3, 1) and (6,4). Include [b]units.[/b]