# Lesson 14

Distances on a Coordinate Plane

### Problem 1

Here are 4 points on a coordinate plane.

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.

### 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 $$j$$.

### Solution

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)