Represent Polygons on the Coordinate Plane Challenge

Grade 6 Math · Unit 7 Challenge Studio (6.GR.3) · Lesson 7-7
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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.Puedo dibujar polígonos a partir de las coordenadas de sus vértices en el plano de coordenadas y usar coordenadas para hallar longitudes de lados y resolver problemas de perímetro y área.

MissionMisión · Orbit StationEstación orbital · night shiftturno de noche

Mission control needs your math.El control de la misión necesita tus matemáticas.

Night shift on Orbit Station: a meteor shower knocked three panels loose. Mission control sends new corner coordinates, a scale in meters and a tight material budget. Every length has to be right on the first try.

Turno de noche en la Estación Órbita: una lluvia de meteoros soltó tres paneles. El control de la misión envía nuevas coordenadas de las esquinas, una escala en metros y un presupuesto de material muy justo. Cada longitud tiene que salir bien al primer intento.

Word bankBanco de palabras 5 words5 palabrasvertex, polygon, perimeter, …vértice, polígono, perímetro, …
vertexvértice
A corner of a polygon. On the grid you name it with an ordered pair, like (4, −2).Una esquina de un polígono. En la cuadrícula se nombra con un par ordenado, como (4, −2).
polygonpolígono
A closed shape made of straight sides. You draw it by plotting the vertices and joining them in order.Una figura cerrada hecha de lados rectos. Se dibuja marcando los vértices y uniéndolos en orden.
perimeterperímetro
The distance around a polygon. Add all of its side lengths.La distancia alrededor de un polígono. Suma las longitudes de todos sus lados.
absolute valuevalor absoluto
How far a number is from 0. To find a side length, subtract the coordinates that are different and use the absolute value.Qué tan lejos está un número del 0. Para hallar la longitud de un lado, resta las coordenadas que son distintas y usa el valor absoluto.
coordinate planeplano cartesiano
A grid made by the x-axis (left and right) and the y-axis (up and down). Each point has an ordered pair.Una cuadrícula formada por el eje x (izquierda y derecha) y el eje y (arriba y abajo). Cada punto tiene un par ordenado.

Stage 1 of 5Etapa 1 de 5

Start StrongEmpieza fuerte

Each rung is harder than the last, and the numbers change every time.

Cada peldaño es más difícil que el anterior y los números cambian cada vez.

  1. 6 fresh problems with new numbers each time (interactive only).

Stage 2 of 5Etapa 2 de 5

Stretch Your ThinkingAmplía tu pensamiento

Plan, solve, then check that your answer makes sense.

Planea, resuelve y revisa que tu respuesta tenga sentido.

  1. Maria is choosing between two store spaces on a grid where each unit is 1 foot and each grid line is 5 feet apart. Space A is a rectangle 25 ft by 40 ft; Space B is 30 ft by 30 ft. Which has more floor area?
    • Space A — 1,000 sq ft vs 900 sq ft
    • Space B — 900 sq ft vs 850 sq ft
    • They are equal
    • Space B — because a square always beats a rectangle
  2. A square has vertices (a, b) and (a, b + s) on one side. Which operation gives the side length for ANY values?
    • Add all four coordinates
    • Subtract the y-coordinates and take the absolute value
    • Multiply a × b
    • Average the coordinates
  3. The park design used width from coordinates, then length from the area, then the scale to place the missing vertices. Design your own version: pick an area and a scale, mark two vertices, and show where the other two go.
  4. Solar panel P on Orbit Station has corners at (−7, 4), (2, 4), (2, −3) and (−7, −3). Each grid unit is 2 meters. A technician runs a border strip all the way around the panel. How many meters of strip does she need?
  5. Three corners of a rectangular docking pad are at (−5, 6), (4, 6) and (4, −2). Each grid unit is 3 meters. What is the area of the pad?
    • 72 m²
    • 216 m²
    • 648 m²
    • 102 m²
  6. Solar array S has corners A(−6, 5), B(1, 5), C(1, 1), D(5, 1), E(5, −3) and F(−6, −3), joined in that order and back to A. Find each side length in units, then the perimeter.
  7. Orbit Station's cargo bay is a rectangle with a perimeter of 34 units. Two of its corners are at (−2, 3) and (6, 3), and the bay extends below that edge. Where are the other two corners?
    • (−2, −6) and (6, −6)
    • (−2, −14) and (6, −14)
    • (−2, 12) and (6, 12)
    • (−2, −23) and (6, −23)

Stage 3 of 5Etapa 3 de 5

InvestigateInvestiga

Use the model to test an idea. Then check it.

Usa el modelo para probar una idea. Luego compruébala.

  1. Sort each job: does it need a side length, a perimeter or an area?
  2. Design a rectangular park that crosses an axis and has an area of exactly 20 square units. List its four vertices as ordered pairs. Show the side lengths with absolute value, then find the perimeter.
  3. 4 fresh problems with new numbers each time (interactive only).

Stage 4 of 5Etapa 4 de 5

Find and FixEncuentra y corrige

Somebody made a mistake. Find the step and fix it.

Alguien cometió un error. Encuentra el paso y corrígelo.

  1. Imani finds the perimeter of rectangle RSTU with vertices R(−6, 2), S(3, 2), T(3, −4) and U(−6, −4).
  2. Luca tapes the edge of panel JKLM, a rectangle with vertices J(1, −2), K(8, −2), L(8, 4) and M(1, 4). He wants to know how many units of tape go all the way around.
  3. Kenji needs the real length of side AB. Vertices A(−4, 1) and B(3, 1) are on a map where each grid unit is 5 meters.
  4. Amara and Dmitri each find the perimeter of the rectangle with vertices (−4, 1), (5, 1), (5, −6) and (−4, −6). Amara says it is 32 units. Dmitri says it is 16 units, because perimeter is the length plus the width. Who is right?
    • Dmitri: the distance around is one length plus one width.
    • Amara: add both lengths twice: 2L + 2W.
    • Both: 16 is just half of 32, so the two answers agree.
    • Neither: the perimeter is 63 units.
  5. What is the best next move?
    • Multiply 30 by 5 × 5 = 25.
    • Stop, because the perimeter is 30.
    • Multiply 9 × 6 to find the answer.
    • Apply the scale: 30 grid units → feet.

Stage 5 of 5Etapa 5 de 5

Prove Your UnderstandingDemuestra tu comprensión

Say how sure you are, solve, then create a problem of your own.

Di qué tan seguro estás, resuelve y luego crea un problema tuyo.

  1. A crew plots four vertices on the grid: A(1, 1), B(5, 1), C(1, 4) and D(5, 4). In which order should they join the points to draw a rectangle without any sides crossing?
    • A, B, C, D, and back to A
    • A, C, B, D, and back to A
    • A, D, B, C, and back to A
    • A, B, D, C, and back to A
  2. A support beam runs from (−3.5, 6) to (4.25, 6) on the station map. How long is the beam in units?
  3. A rectangular lab module has its top edge from (−8, 3) to (1, 3). Its area is 45 square units, and the module extends below the top edge. What is the y-coordinate of its bottom edge?
  4. Three vertices of a rectangle are P(−4, −1), Q(5, −1) and R(5, 6). What are the coordinates of the fourth vertex, S?
    • (6, −4)
    • (−4, 6)
    • (−4, −6)
    • (4, 6)
  5. Two panels are drawn on the grid. Panel X has vertices (−6, 4), (6, 4), (6, 1) and (−6, 1). Panel Y has vertices (−3, −1), (3, −1), (3, −7) and (−3, −7). Which statement is true?
    • The perimeters are the same, but X has the greater area.
    • X has the greater area and the longer perimeter.
    • The areas are the same, but X has the longer perimeter.
    • The areas and the perimeters are both the same.
  6. Create your own rectangle on the coordinate plane. Give its four vertices, and make sure at least one coordinate is negative. Find the length of each side and the perimeter, and explain how you know which coordinates to use.