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.
Close

Information: IM 8.8.11 Lesson: Finding Distances in the Coordinate Plane