# Lesson 13

Distances and Shapes on the Coordinate Plane

Let’s explore distance on the coordinate plane.

### Problem 1

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 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

1. How much higher is 500 than 400 m?
2. How much higher is 500 than -400 m?
3. What is the change in elevation from 8,500 m to 3,400 m?
4. What is the change in elevation between 8,500 m and -300 m?
5. How much higher is -200 m than 450 m?
(From Unit 7, Lesson 10.)

### Problem 4

1. Plot and connect the following points to form a polygon.

$$(\text-3, 2), (2, 2), (2, \text-4), (\text-1, \text-4), (\text-1, \text-2), (\text-3, \text-2), (\text-3, 2)$$

2. Find the perimeter of the polygon.

### Problem 5

For each situation, select all the equations that represent it. Choose one equation and solve it.

1. Jada’s cat weighs 3.45 kg. Andre’s cat weighs 1.2 kg more than Jada’s cat. How much does Andre’s cat weigh?

$$x = 3.45 + 1.2$$

$$x = 3.45 - 1.2$$

$$x +1.2 = 3.45$$

$$x-1.2=3.45$$

2. Apples cost \$1.60 per pound at the farmer’s market. They cost 1.5 times as much at the grocery store. How much do the apples cost per pound at the grocery store?

$$y = (1.5) \boldcdot (1.60)$$

$$y = 1.60 \div 1.5$$

$$(1.5)y = 1.60$$

$$\frac{y}{1.5} = 1.60$$

(From Unit 4, Lesson 4.)