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 \((\text-4, \text-5)\)

  1. What is the length and width of this rectangle?
  2. What is the perimeter of the rectangle?
  3. 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.

Problem 3

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

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

    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.

  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.

  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 6, Lesson 4.)