Lesson 7.7Designing Polygons with a Scale
Start hereWords, worked example, and sentence starters
Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| vertexSpanish: vértice | A corner point of a polygon, named by an ordered pair on the coordinate plane. | named by an ordered pair |
| polygonSpanish: polígono | A closed figure made of line segments; on the plane you draw it by plotting the vertices and connecting them in order. | Plot (2, 4), (5, 4), (5, −4), (2, −4) and join them — a rectangle appears. |
| perimeterSpanish: perímetro | The total distance around a polygon — the sum of all its side lengths. | add every side length |
| distance between verticesSpanish: distancia entre vértices | When two vertices share an x- or y-coordinate, the distance between them is the absolute difference of the other coordinates. | (2, 4) and (5, 4) share y, so the side is |5 − 2| = 3 units. |
| scaleSpanish: escala | What one grid unit stands for in the real situation. | 1 unit = 25 feet |
| Side lengthSpanish: Longitud del lado | The distance between two vertices that are joined by a side. | Found with absolute value when the points share a coordinate. |
How it worksWorked exampleusing a scale to find a missing dimension
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A rectangular lot needs an area of 30,000 square feet. Two of its vertices sit at (−2.5, 10.5) and (−2.5, 4.5). Each grid unit stands for 25 feet.
- The x-coordinates match, so count the y-values: 10.5 − 4.5 gives six units.
- Each unit stands for 25 feet, so that known side measures 150 feet.
- Divide the area by that side: 30,000 ÷ 150 = 200 feet for the other side.
- Turn 200 feet back into grid units: 200 ÷ 25 = eight units.
Answer: The lot measures 150 feet by 200 feet, drawn as six units by eight units on the grid.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A rectangular court needs an area of 28,800 square feet. Two of its vertices sit at (5.5, −1.5) and (5.5, −13.5). Each grid unit stands for 20 feet.
- The -coordinates match, so count the y-values: units apart.
- Each unit stands for feet, so that known side measures feet.
- Divide the area by that side: ÷ = feet.
- Turn that length back into grid units: ÷ = units.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- Each grid unit stands for , so units equals .
- The missing vertex is because .
- The area is square because I multiplied by .
- I changed units into before I .
Word bank scalegrid unitvertexdimensionsareaperimeterconvertmultiplydividerectanglesquare feetside length
Watch outA common mistake
Subtracting coordinates without the absolute value — from y = 3 down to y = −3.75 the distance is 3 + 3.75 = 6.75 units, not 3.75 − 3 = 0.75. Distances that cross zero are the whole reason the absolute value is there.
Lesson 7.7Designing Polygons with a Scale
Apply Day · Version ASupported practice
Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.
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1Complete each step, then write the final answer.
Find the length of the side from (−3, 5) to (4, 5).
Show your workHint Both points have y = 5. Add the distances from 0.
Final answer: -
2Complete each step, then write the final answer.
A rectangle has vertices (−2, 1), (3, 1), (3, −3) and (−2, −3). Find its perimeter.
Show your workHint Find one side across and one side up and down. Then add all four sides.
Final answer: -
3Complete each step, then write the final answer.
A rectangle has vertices (−2, 5), (4, 5), (4, 2) and (−2, 2). Find its area.
Show your workHint Find the length and the width. Then multiply.
Final answer:
Lesson 7.7Designing Polygons with a Scale
Apply Day · Version BCore practice
Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.
-
1Complete each step, then write the final answer.
Sam says the rectangle with vertices (−5, 1), (3, 1), (3, 4) and (−5, 4) has a perimeter of 8 + 3 = 11 units. Is he right? What is the perimeter?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A rectangle has vertices (−6, 2), (−1, 2) and (−1, −3). The fourth vertex is (−6, ?). What is the missing y-coordinate?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A rectangle has vertices (−3, 6), (3, 6), (3, 2) and (−3, 2). Find its perimeter.
Show your workFinal answer:
Lesson 7.7Designing Polygons with a Scale
Apply Day · ChallengeExtension
Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.
-
1Circle the letter of the best answer. Show how you know.
A rectangle has vertices at (1, 1), (7, 1), (7, 5), and (1, 5). What is its perimeter?
- A10 units
- B12 units
- C20 units
- D24 units
FormulaPut the numbers inWork it outAnswer with its unit -
2Circle the letter of the best answer. Show how you know.
Space A has corners (0, 0), (20, 0), (20, 20) and (0, 20). Space B has corners (0, 0), (30, 0), (30, 12) and (0, 12). Each unit is 1 foot. Which space has more floor area?
- ASpace A
- BSpace B
- CThey have the same area.
Show your work -
3Complete each step, then write the final answer.
Three vertices of a rectangle are (−4, 2), (4, 2) and (4, −3). What is the area of the rectangle?
Show your workFinal answer: