IM 8.8.11 Lesson: Finding Distances in the Coordinate Plane
Order the following pairs of coordinates from closest to farthest apart. Be prepared to explain your reasoning.
a. [math](2,4)[/math] and [math](2,10)[/math][br]b. [math](\text{-}3,6)[/math] and [math](5,6)[/math][br]c. [math](-12,-12)[/math] and [math](-12,-1)[/math][br]d. [math](7,0)[/math] and [math](7,-9)[/math][br]e. [math](1,-10)[/math] and [math](-4,-10)[/math]
Name another pair of coordinates that would be closer together than the first pair on your list.
Name another pair of coordinates that would be farther apart than the last pair on your list.
Find the distances between the three points shown.
Which figure do you think has the longer perimeter?
[img]data:image/png;base64,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[/img][br]
Select one figure and calculate its perimeter. Your partner will calculate the perimeter of the other. Were you correct about which figure had the longer perimeter?
[code][/code][size=150][code][/code]Quadrilateral [math]ABCD[/math] has vertices at [math]A=(-5,1)[/math], [math]B=(-4,4)[/math], [math]C=(2,2)[/math] and[math]D=(1,-1)[/math].[/size][br][br][size=100]Use the Pythagorean Theorem to find the lengths of sides [math]AB[/math], [math]BC[/math], [math]CD[/math], and [math]AD[/math].[/size]
Use the Pythagorean Theorem to find the lengths of the two diagonals, [math]AC[/math] and [math]BD[/math].
Explain why quadrilateral [math]ABCD[/math] is a rectangle.
For this activity, you will work with a small group.
Have each person in your group select one of the sets of coordinate pairs shown here. Then calculate the length of the line segment between those two coordinates. Once the values are calculated, have each person in the group briefly share how they did their calculations.[br][br][math](-3,1)[/math] and [math](5,7)[/math][br][math](-1,-6)[/math] and [math](5,2)[/math][br][math](-1,2)[/math] and [math](5,-6)[/math][br][math](-2,-5)[/math] and [math](6,1)[/math][br][br]How does the value you found compare to the rest of your group?
In your own words, write an explanation to another student for how to find the distance between any two coordinate pairs.
IM 8.8.11 Practice: Finding Distances in the Coordinate Plane
The right triangles are drawn in the coordinate plane, and the coordinates of their vertices are labeled. For each right triangle, label each leg with its length.
Find the distance between each pair of points. If you get stuck, use the applet below.
[math]M=(0,-11)[/math] and [math]P=(0,2)[/math]
[math]A=(0,0)[/math] and[math]B=(-3,4)[/math]
[math]C=(8,10)[/math] and [math]D=(0,-6)[/math]
If you get stuck, try plotting the points on in this applet.
Find an object that contains a right angle. This can be something in nature or something that was made by humans or machines.
Measure the two sides that make the right angle. Then measure the distance from the end of one side to the end of the other. Record those measurements here.
Draw a diagram of the object, including the measurements.
Use the Pythagorean Theorem to show that your object really does have a right angle.
Which line has a slope of 0.625, and which line has a slope of 1.6? Explain why the slopes of these lines are 0.625 and 1.6.
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[/img]
Write an equation for the graph.
[img]data:image/png;base64,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[/img]