Mathematics
Grade 6
15 min
Reflections: graph the image (Tutorial Only)
Reflections: graph the image (Tutorial Only)
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define key terms related to reflections, such as pre-image, image, and line of reflection.
Identify the line of reflection (x-axis, y-axis, or horizontal/vertical lines).
Graph the reflection of a single point across the x-axis or y-axis.
Graph the reflection of a single point across a horizontal or vertical line.
Graph the reflection of a polygon (triangle or quadrilateral) across the x-axis or y-axis.
Graph the reflection of a polygon across a horizontal or vertical line.
Label the vertices of the reflected image using prime notation.
Have you ever looked in a mirror and seen an exact copy of yourself, but flipped? 🪞 That's a reflection! In math, we can do the same thing with shapes on a graph.
In this tutorial, you'll learn how to 'f...
2
Key Concepts & Vocabulary
TermDefinitionExample
ReflectionA transformation that 'flips' a figure over a line, creating a mirror image. The size and shape of the figure do not change.Flipping a triangle over the x-axis to get a new triangle below it.
Pre-imageThe original figure or point before it has been reflected.If point A is at (2, 3) before reflection, A is the pre-image.
ImageThe new figure or point created after the reflection. It is usually labeled with a prime symbol (').If point A is at (2, 3) and is reflected to A' at (2, -3), A' is the image.
Line of ReflectionThe line across which a figure is reflected. It acts like a mirror.The x-axis, the y-axis, or a line like y=2 or x=-1 can be a line of reflection.
Coordinate PlaneA grid formed by two perpendicular number lines (x-axis an...
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Core Formulas
Reflection Across the x-axis
$(x, y) \rightarrow (x, -y)$
When reflecting a point or figure across the x-axis, the x-coordinate stays the same, and the y-coordinate changes to its opposite sign. The distance from the x-axis remains the same, but on the opposite side.
Reflection Across the y-axis
$(x, y) \rightarrow (-x, y)$
When reflecting a point or figure across the y-axis, the y-coordinate stays the same, and the x-coordinate changes to its opposite sign. The distance from the y-axis remains the same, but on the opposite side.
Reflection Across a Horizontal Line ($y=k$)
Count the vertical distance from the point to the line $y=k$. The reflected point will be the same distance from $y=k$ on the opposite side. The x-coordinate stays the same. The new y-coordinate is $...
5 more steps in this tutorial
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Challenging
Triangle TUV has vertices T(-5, 6), U(-2, 6), and V(-2, 3). What are the coordinates of the image, T'U'V', after a reflection across the line y = 2?
A.T'(-5, -2), U'(-2, -2), V'(-2, 1)
B.T'(-5, -4), U'(-2, -4), V'(-2, -1)
C.T'(5, 6), U'(2, 6), V'(2, 3)
D.T'(-5, 8), U'(-2, 8), V'(-2, 5)
Challenging
Quadrilateral WXYZ has vertices W(2, 5), X(4, 5), Y(5, 3), and Z(1, 3). What are the coordinates of the image, W'X'Y'Z', after a reflection across the line x = -1?
A.W'(-3, 5), X'(-5, 5), Y'(-6, 3), Z'(-2, 3)
B.W'(2, -7), X'(4, -7), Y'(5, -5), Z'(1, -5)
C.W'(-4, 5), X'(-6, 5), Y'(-7, 3), Z'(-3, 3)
D.W'(-2, 5), X'(-4, 5), Y'(-5, 3), Z'(-1, 3)
Challenging
Point A is at (5, -3). It is reflected across the x-axis to create A'. Then, A' is reflected across the y-axis to create A''. What are the coordinates of A''?
A.(-5, 3)
B.(5, 3)
C.(-5, -3)
D.(5, -3)
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