Coordinate Reflection Task Cards
Cut along dashed center line Coordinate Geometry • Task Card Set A Page 1 of 5
CARD 01 Reflection Over the x-Axis
Level 1 • Axis Rule
x y 4 -4 4 -4 J K L
Pre-image $\triangle JKL$ Line: $y = 0$
Triangle $\triangle JKL$ is graphed on the coordinate plane. Reflect $\triangle JKL$ across the x-axis.
PART A • Identify Pre-image Coordinates:
\(J(2, 5)\)
\(K(5, 2)\)
\(L(2, 1)\)
PART B • Algebraic Mapping Rule:
Across the x-axis: \((x, y) \rightarrow (\underline{\quad}, \underline{\quad})\)
PART C • Image Coordinates:
Determine coordinates of image \(\triangle J'K'L'\):
\(J'(\quad, \quad)\)
\(K'(\quad, \quad)\)
\(L'(\quad, \quad)\)
Reasoning Prompt: Which coordinate value stays the same after reflecting across the x-axis? Why does this make geometric sense?
Cut Line
CARD 02 Reflection Over the y-Axis
Level 1 • Axis Rule
x y 4 -4 4 -4 W X Y Z
Pre-image \(WXYZ\) Line: $x = 0$
Quadrilateral \(WXYZ\) lies in Quadrant II. Reflect the entire quadrilateral across the y-axis into Quadrant I.
PART A • Algebraic Mapping Rule:
Across the y-axis: \((x, y) \rightarrow (\underline{\quad}, \underline{\quad})\)
PART B • Image Vertices:
Apply the rule to write the image coordinates:
W(-5, 4) → W'( , )
X(-2, 5) → X'( , )
Y(-1, 2) → Y'( , )
Z(-4, 1) → Z'( , )
Perpendicular Distance Check: Verify that vertex $W$ and vertex $W'$ are each exactly 5 units away from the $y$-axis.
Cut along dashed center line Coordinate Geometry • Task Card Set B Page 2 of 5
CARD 03 Reflection Over Line x = -1
Level 2 • Vertical Line
x = -1 x y 4 -4 4 -4 A B C
Pre-image $\triangle ABC$ Line: $x = -1$
Reflect $\triangle ABC$ across the vertical line \(x = -1\). Notice this line is parallel to the \(y\)-axis.
PART A • Count Horizontal Distance to \(x = -1\):
Pt A: 2 units right
Pt B: ___ units right
Pt C: ___ units right
PART B • New Coordinates of \(\triangle A'B'C'\):
Count the exact same distance to the left of \(x = -1\):
A(1, 4) A'(-3, 4)
B(4, 3) B'( , )
C(2, 1) C'( , )
Notice: Does the \(y\)-coordinate change during a reflection across any vertical line \(x = k\)? Yes / No. Explain why.
Cut Line
CARD 04 Reflection Over Line y = 1
Level 2 • Horizontal Line
y = 1 x y 4 -4 4 -4 D E F
Pre-image $\triangle DEF$ Line: $y = 1$
Reflect $\triangle DEF$ across the horizontal line \(y = 1\).
PART A • Vertical Distance Analysis:
Point $E$ is at $y = 5$. The line of reflection is at $y = 1$. The vertical distance is $5 - 1 = 4$ units above the line.
Image $E'$ must be 4 units below $y = 1 \rightarrow 1 - 4 = \mathbf{-3}$.
PART B • Complete Image Vertices:
D(-4, 3) D'( , )
E(-1, 5) E'(-1, -3)
F(-2, 2) F'( , )
Midpoint Formula Connection: Verify that the midpoint between $D(-4, 3)$ and $D'$ has a $y$-coordinate of exactly $1$.
Cut along dashed center line Coordinate Geometry • Task Card Set C Page 3 of 5
CARD 05 Mystery Line of Reflection
Level 3 • Detective Challenge
x y M N P M' N' P'
Pre-image Image Find the Line!
$\triangle MNP$ was reflected to produce $\triangle M'N'P'$. Find the exact equation of the line of reflection!
PART A • Coordinate Comparison:
Pre-image: \(M(-5, 2), P(-1, 1)\)
Image: \(M'(-5, -4), P'(-1, -3)\)
PART B • Find the Midpoints:
Calculate the midpoint between $M$ and $M'$:
\(\text{Midpoint} = \left(\frac{-5 + (-5)}{2}, \frac{2 + (-4)}{2}\right) = (-5, \mathbf{\quad})\)
PART C • Equation of the Reflection Line:
The line of reflection is: y = ______
Perpendicular Bisector Property: Why does the line of reflection always pass through the midpoints of segments connecting corresponding vertices?
Cut Line
CARD 06 Reflection Over Diagonal Line y = x
Level 3 • Diagonal Swap
y = x x y 4 -4 4 -4 R S T
Pre-image $\triangle RST$ Line: $y = x$
Reflect $\triangle RST$ across the diagonal line \(y = x\).
PART A • The Coordinate Swap Rule:
Because $y$ equals $x$ on this line, every $x$-coordinate and $y$-coordinate trade places!
\((x, y) \rightarrow (y, x)\)
PART B • Image Coordinates:
R(1, 4) R'(4, 1)
S(4, 5) S'( , )
T(3, 1) T'( , )
Invariant Points: What would happen to a point like $(3, 3)$ when reflected across $y = x$? What is this type of point called?
Cut along dashed center line Coordinate Geometry • Task Card Set D Page 4 of 5
CARD 07 Double Reflection & Composite Rules
Level 4 • Composite
x y P(-3, 4) P'(3, 4) P''(3, -4) (0,0)
Two Perpendicular Reflections
Point \(P(-3, 4)\) undergoes a sequence of two reflections: first across the y-axis, and then across the x-axis.
PART A • Step-by-Step Mapping:
Step 1: \(P(-3, 4) \xrightarrow{\text{reflect } y\text{-axis}} P'(3, 4)\)
Step 2: \(P'(3, 4) \xrightarrow{\text{reflect } x\text{-axis}} P''(3, -4)\)
PART B • Try Another Point:
Apply this double reflection to vertex \(Q(-5, -2)\):
After y-axis reflection Q'( , )
After x-axis reflection Q''( , )
PART C • Discovery Question:
What single rigid transformation maps \((x, y) \rightarrow (-x, -y)\) directly?
Big Idea: A reflection across the $y$-axis followed by the $x$-axis is equivalent to a 180° rotation around the origin!
Cut Line
CARD 08 Error Detective • Spot the Mistake
Level 4 • Critique Reasoning
x y x = 2 V(5, 3) Jordan's V' Correct V' 3 units
Jordan's Error Correct Point
Jordan's Claim:
"To reflect \(V(5, 3)\) across \(x = 2\), I subtract 2 from the x-coordinate because the line is at 2. So my image is \(V'(3, 3)\)."
PART A • Identify the Misconception:
What did Jordan do wrong conceptually?
PART B • Calculate True Distance:
Horizontal distance from \(V(5, 3)\) to line \(x = 2\): 5 - 2 = 3 units
PART C • Determine Correct Image:
Count 3 units to the left of \(x = 2\): V'( , )
Teacher Tip: A reflection creates a mirror image equidistant from the reflection line—never simply offset by the line's coordinate!
Reflections on the Coordinate Plane
Task Card Station Recording & Response Sheet
8 Challenge Cards
Student Name
Date
Class / Period
Final Score
/ 24 pts
CARD 01 • Reflect over x-Axis 3 pts
Rule: \((x, y) \rightarrow (\quad, \quad)\)
\(J'(\quad, \quad)\)
\(K'(\quad, \quad)\)
\(L'(\quad, \quad)\)
Which value stays constant? ________________
CARD 02 • Reflect over y-Axis 3 pts
Rule: \((x, y) \rightarrow (\quad, \quad)\)
\(W'(\quad, \quad)\)
\(X'(\quad, \quad)\)
\(Y'(\quad, \quad)\)
\(Z'(\quad, \quad)\)
Distance from \(y\)-axis to \(W'\): ______ units
CARD 03 • Reflect over line x = -1 3 pts
Distance from \(B(4, 3)\) to line \(x = -1\): _____ units
\(A'(-3, 4)\)
\(B'(\quad, \quad)\)
\(C'(\quad, \quad)\)
Did \(y\)-values change? Yes / No
CARD 04 • Reflect over line y = 1 3 pts
Distance from \(D(-4, 3)\) to line \(y = 1\): _____ units
\(D'(\quad, \quad)\)
\(E'(-1, -3)\)
\(F'(\quad, \quad)\)
Midpoint \(y\)-value of segment \(DD'\): \(y =\) _____
CARD 05 • Mystery Line Equation 3 pts
Midpoint of \(M(-5, 2)\) and \(M'(-5, -4)\):
\(\text{Midpoint} = (-5, \mathbf{\quad})\)
Line of Reflection: \(y =\) ______
Horizontal or Vertical line? ________________
CARD 06 • Diagonal Line y = x 3 pts
Rule: \((x, y) \rightarrow (y, x)\)
\(R'(4, 1)\)
\(S'(\quad, \quad)\)
\(T'(\quad, \quad)\)
What happens to point \((7, 7)\)? ________________
CARD 07 • Double Reflection 3 pts
For \(Q(-5, -2)\):
\(Q'(\quad, \quad)\)
\(Q''(\quad, \quad)\)
Equivalent single transformation: ______________
Overall rule: \((x, y) \rightarrow (\mathbf{\quad}, \mathbf{\quad})\)
CARD 08 • Error Detective 3 pts
Jordan's error explanation:
Correct \(V'\): V'( , )
Correct distance to line: ______ units
Reflection Rules Quick Reference:
x-axis: \((x, -y)\) y-axis: \((-x, y)\) y = x: \((y, x)\) x = k / y = k: Equal distance from line
