Distances on a Coordinate Plane: IM 6.7.14
[url=https://im.kendallhunt.com/MS/teachers/1/7/14/preparation.html]“Distances on a Coordinate Plane”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.7.14
- IM 6.7.14 Lesson: Distances on a Coordinate Plane
- Practice 6.7.14
- IM 6.7.14 Practice: Distances on a Coordinate Plane
IM 6.7.14 Lesson: Distances on a Coordinate Plane
Plot points in your assigned quadrant and label them with their coordinates.
Write the coordinates of each point shown in the graph below. [br][list][*][math]A=[/math][br][/*][*][math]B=[/math][br][/*][*][math]C=[/math][br][/*][*][math]D=[/math][br][/*][*][math]E=[/math][br][/*][/list]
Answer these questions for each pair of points.
[list][*]How are the coordinates the same? How are they different?[/*][*]How far away are they from the y-axis? To the left or to the right of it?[/*][*]How far away are they from the x-axis? Above or below it?[/*][/list][br][math]A[/math] and [math]B[/math]
[math]B[/math] and [math]D[/math]
[math]A[/math] and [math]D[/math]
Point F has the same coordinates as point C, except its y-coordinate has the opposite sign. Plot point F on the coordinate plane and label it with its coordinates.
How far away are[math]F[/math] and [math]C[/math] from the [math]x[/math]-axis?[br]
What is the distance between [math]F[/math] and [math]C[/math]?
Point G has the same coordinates as point E, except its x-coordinate has the opposite sign. Plot point G on the coordinate plane and label it with its coordinates.
How far away are [math]G[/math] and [math]E[/math] from the [math]y[/math]-axis?
What is the distance between [math]G[/math] and [math]E[/math]?
Point [math]H[/math] has the same coordinates as point [math]B[/math], except both of its coordinates have the opposite signs. In which quadrant is point [math]H[/math]?
Label each point with its coordinates.
Find the distance between each of the following pairs of points.
Point [math]B[/math] and [math]C[/math]
Point [math]D[/math] and [math]B[/math]
Point [math]D[/math] and [math]E[/math]
Which of the points are 5 units from [math]\left(-1.5,-3\right)[/math]?
Which of the points are 2 units from [math]\left(0.5,-4.5\right)[/math]?
Plot a point that is both 2.5 units from A and 9 units from E. Label that point F and write down its coordinates.
Priya says, “There are exactly four points that are 3 units away from [math]\left(-5,0\right)[/math].” Lin says, “I think there are a whole bunch of points that are 3 units away from [math]\left(-5,0\right)[/math].”[br][br]Do you agree with either of them? Explain your reasoning.
IM 6.7.14 Practice: Distances on a Coordinate Plane
Here are 4 points on a coordinate plane. Label each point with its coordinates.
[list=1][*]Label each point with its coordinates.[/*][*]Plot a point that is 3 units from point [math]K[/math]. Label it [math]P[/math].[/*][*]Plot a point that is 2 units from point [math]M[/math]. Label it [math]W[/math].[/*][/list]
Each set of points are connected to form a line segment. What is the length of each?
A = [math]\left(3,5\right)[/math] and B = [math]\left(3,6\right)[/math]
C = [math]\left(-2,-3\right)[/math] and D = [math]\left(-2,-6\right)[/math]
E = [math]\left(-3,1\right)[/math] and F = [math]\left(-3,-1\right)[/math]
On the coordinate plane, plot four points that are each 3 units away from point P = (-2, -1). Write the coordinates of each point.
Noah’s recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.
Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, [math]t[/math], that he needs to prepare. Write an equation that shows how Noah can find [math]s[/math], the number of liters of soda water, if he knows [math]t[/math].
Sometimes the school purchases a certain number, [math]j[/math], of liters of orange juice and Noah needs to figure out how much sparkling orange juice he can make. Write an equation that Noah can use to find [math]t[/math] if he knows [math]j[/math].
For a suitcase to be checked on a flight (instead of carried by hand), it can weigh at most 50 pounds. Andre’s suitcase weighs 23 kilograms.
Can Andre check his suitcase? Explain or show your reasoning. (Note: 10 kilograms [math]\approx[/math] 22 pounds)