Reflect Points Across Axes Challenge

Grade 6 Math · Unit 7 Challenge Studio (6.NOS.7) · Lesson 7-9
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I can reflect points across the x-axis and y-axis on the coordinate plane.Puedo reflejar puntos sobre el eje x y el eje y en el plano de coordenadas.

MissionMisión · Maker WorkshopTaller de creadores · night shiftturno de noche

Build it right.Constrúyelo bien.

Late-night rush in the Maker Workshop: a client wants a sign that is perfectly symmetrical, and the wood is too expensive to waste. Check every mirror point before the laser fires.

Trabajo urgente de noche en el Taller de Creadores: un cliente quiere un letrero perfectamente simétrico, y la madera es demasiado cara para desperdiciarla. Revisa cada punto del espejo antes de que dispare el láser.

Word bankBanco de palabras 5 words5 palabrasreflection, x-axis, y-axis, …reflexión, eje x, eje y, …
reflectionreflexión
A flip of a point or figure across a line, like a mirror. The image is the same distance from the line, on the other side.Un volteo de un punto o una figura sobre una línea, como un espejo. La imagen queda a la misma distancia de la línea, del otro lado.
x-axiseje x
The horizontal number line. Reflecting across it changes the sign of y: (x, y) → (x, −y).La recta numérica horizontal. Reflejar sobre ella cambia el signo de y: (x, y) → (x, −y).
y-axiseje y
The vertical number line. Reflecting across it changes the sign of x: (x, y) → (−x, y).La recta numérica vertical. Reflejar sobre ella cambia el signo de x: (x, y) → (−x, y).
symmetrysimetría
A figure has symmetry when one side is the mirror image of the other side.Una figura tiene simetría cuando un lado es la imagen en espejo del otro lado.
perpendicularperpendicular
Two lines that meet at a square corner (90°). A point and its image are joined by a segment perpendicular to the axis.Dos líneas que se cruzan formando una esquina cuadrada (90°). Un punto y su imagen se unen con un segmento perpendicular al eje.

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. Find the Reflection Error
  2. A triangle has vertices at A(1, 2), B(4, 2), and C(4, 6). If you reflect the entire triangle over the y-axis, what are the new vertices? What do you notice about the size and shape of the reflected triangle compared to the original?
  3. Five holes are marked on a workshop panel: A(−5, 2), B(5, −2), C(−2, 5), D(5, 2) and E(2, −5). Which two holes are reflections of each other across the y-axis?
    • B and D
    • A and D
    • A and B
    • A and E
  4. A rectangular tile has vertices (2, 1), (7, 1), (7, 4) and (2, 4). A copy of the tile is made by reflecting it across the y-axis. How many units apart are the two tiles at their closest edges?
  5. Complete the laser's reflection log. Each row shows a point, the axis it is reflected across, and its image. Fill in every empty cell.
  6. A bracket ends at (6, −9) after two reflections: first across the x-axis, then across the y-axis. Where did the bracket start?
    • (−6, 9)
    • (6, 9)
    • (−6, −9)
    • (6, −9)

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. Point P is at (4, 3). Sort each point by how it is related to P.
  2. Create an emblem with four points in Quadrant I. Reflect each original point across the y-axis. Then reflect each original point across the x-axis. List the coordinates of your reflected points. Explain how the distance from the mirror line proves your reflections are correct.
  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. Dmitri reflects the point (−4, 9) across the x-axis.
  2. Lena reflects the point (6, −5) across the y-axis.
  3. Kai reflects a bolt at (3, 8) across the y-axis.
  4. Noor, Mateo and Lin reflect the point (5, 0) across the x-axis. Noor says the reflection is (5, 0). Mateo says it is (−5, 0). Lin says it is (0, 5). Who is right?
    • Mateo: every reflection changes one of the signs.
    • Lin: the two coordinates trade places.
    • Nobody: a point on an axis has no reflection.
    • Noor: on the x-axis, reflection stays fixed.
  5. What is the best next move?
    • Stop, because one image point shows the whole triangle.
    • Reflect B and C the same way, one at a time.
    • Reflect only C, the vertex farthest from the axis.
    • Change the signs of the x-coordinates of B and C.
  6. 1 fresh problem with new numbers each time (interactive only).

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. Point P is in Quadrant II. P is reflected across the x-axis. In which quadrant is the reflection of P?
    • Quadrant I
    • Quadrant II
    • Quadrant III
    • Quadrant IV
  2. A rectangle has vertices (−7, 2), (−3, 2), (−3, 5) and (−7, 5). It is reflected across the x-axis. What is the y-coordinate of the TOP edge of the image?
  3. Triangle JKL has vertices J(2, 1), K(6, 1) and L(2, 5). Which list gives the vertices J′, K′ and L′ of its reflection across the y-axis?
    • J′(2, −1), K′(6, −1), L′(2, −5)
    • J′(−2, −1), K′(−6, −1), L′(−2, −5)
    • J′(−2, 1), K′(6, 1), L′(2, 5)
    • J′(−2, 1), K′(−6, 1), L′(−2, 5)
  4. A point in Quadrant I and its reflection across the y-axis are 14 units apart. The point is 3 units above the x-axis. What are the coordinates of the point?
    • (7, 3)
    • (14, 3)
    • (3, 7)
    • (−7, 3)
  5. A kite on the grid has vertices (0, 6), (3, 2), (0, −2) and (−3, 2). Which statement is true?
    • It is symmetric across the x-axis, but not across the y-axis.
    • It is symmetric across the y-axis, but not across the x-axis.
    • It is symmetric across both axes.
    • It is not symmetric across either axis.
  6. Choose a point that is not on either axis. Reflect it across the x-axis, across the y-axis, and across both axes. List the three images, then explain what stays the same and what changes each time, using the words reflection and axis.
  7. 1 fresh problem with new numbers each time (interactive only).