Lesson 15
Shapes on the Coordinate Plane
Let’s use the coordinate plane to solve problems and puzzles.
Problem 1
The coordinates of a rectangle are \((3, 0)\), \((3, \text-5)\), \((\text-4, 0)\) and \((\text-4, \text-5)\)
- What is the length and width of this rectangle?
- What is the perimeter of the rectangle?
- What is the area of the rectangle?
Problem 2
Draw a square with one vertex on the point \((\text-3,5)\) and a perimeter of 20 units. Write the coordinates of each other vertex.
![A coordinate plane with the origin labeled "O". Both axes have the numbers negative 5 through 5 indicated.](https://staging-cms-im.s3.amazonaws.com/1XVwuMh8xnpshaF2uAKR1dmA?response-content-disposition=inline%3B%20filename%3D%226-6.7.EA.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%276-6.7.EA.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T171258Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=677efd875e93378b164ff47e1b81ef19f1bb86ea8cec748b7527d4af5ee5dab3)
Problem 3
- Plot and connect the following points to form a polygon.
\((\text-3, 2), (2, 2), (2, \text-4), (\text-1, \text-4), (\text-1, \text-2), (\text-3, \text-2), (\text-3, 2)\)
-
Find the perimeter of the polygon.
Problem 4
For each situation, select all the equations that represent it. Choose one equation and solve it.
-
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?
\(x = 3.45 + 1.2\)
\(x = 3.45 - 1.2\)
\(x +1.2 = 3.45\)
\(x-1.2=3.45\)
-
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?
\(y = (1.5) \boldcdot (1.60)\)
\(y = 1.60 \div 1.5\)
\((1.5)y = 1.60\)
\(\frac{y}{1.5} = 1.60\)