Lesson 14

Distances on a Coordinate Plane

Let’s explore distance on the coordinate plane.

Problem 1

Here are 4 points on a coordinate plane.

Coordinate plane, origin O, x and y axes marked by ones. Point K is three left, 3 up. Point X is 3 right, 2 up. Point M is 5 left, 4 down. Point Y is 2 right, 3 down.
  1. Label each point with its coordinates.
  2. Plot a point that is 3 units from point \(K\). Label it \(P\).
  3. Plot a point that is 2 units from point \(M\). Label it \(W\).

Problem 2

Each set of points are connected to form a line segment. What is the length of each?

  1. A = \((3, 5)\) and B = \((3, 6)\)
  2. C = \((\text-2, \text-3)\) and D = \((\text-2, \text-6)\)
  3. E = \((\text-3, 1)\) and F = \((\text-3, \text-1)\)

Problem 3

On the coordinate plane, plot four points that are each 3 units away from point \(P=(\text-2, \text-1)\). Write the coordinates of each point.

A coordinate plane with the origin labeled "O." The x-axis has the numbers negative 7 through 7 indicated. The y-axis has the numbers negative 5 through 5 indicated.

Problem 4

Noah’s recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

  1. Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, \(t\), that he needs to prepare. Write an equation that shows how Noah can find \(s\), the number of liters of soda water, if he knows \(t\).

  2. Sometimes the school purchases a certain number, \(j\), 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 \(t\) if he knows \(j\).
(From Unit 6, Lesson 16.)

Problem 5

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 \(\approx\) 22 pounds)

(From Unit 3, Lesson 4.)