Grid Gliders Worksheet
Geometry Workshop Coordinate Transformations
Grid Gliders: Translations
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Page: 1 of 2
Translation: A rigid motion that slides every point of a figure the same distance in the same direction. The pre-image and image are congruent (\(\Delta ABC \cong \Delta A'B'C'\)).
Algebraic Rule: \((x, y) \to (x + a, y + b)\) — where \(+a\) slides right, \(-a\) slides left, \(+b\) slides up, and \(-b\) slides down.
Problem 1 Identify Translation
How many units has the object been translated and in what direction?
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C A' B' C'
Vertices
A (1, 4) → A' (-5, 4)
B (4, 0) → B' (-2, 0)
C (1, 0) → C' (-5, 0)
Translation:
Coordinate Rule: \((x, y) \to (\) , \()\)
How do the new ordered pairs relate to the original?
Problem 2 Identify Translation
How many units has the object been translated and in what direction?
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C A' B' C'
Vertices
A (-3, 5) → A' (0, -2)
B (0, 1) → B' (3, -6)
C (-3, 1) → C' (0, -6)
Translation:
Coordinate Rule: \((x, y) \to (\) , \()\)
How do the new ordered pairs relate to the original?
Problem 3 Graph Translation
Translate the figure 4 units to the right. Graph and label \(\Delta A'B'C'\).
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C
Original Vertices
A (-3, 5)
B (-2, 1)
C (-4, 1)
Coordinate Rule:
\((x, y) \to (x+4, y)\)
New Image Coordinates:
A' (___, ___)
B' (___, ___)
C' (___, ___)
Tip: Add 4 to each x-coordinate, then plot the new vertices on the grid above.
Problem 4 Graph Translation
Translate the figure 3 units left and 4 units up. Graph and label \(\Delta A'B'C'\).
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C
Original Vertices
A (2, -1)
B (3, -4)
C (1, -4)
Coordinate Rule:
\((x, y) \to (x-3, y+4)\)
New Image Coordinates:
A' (___, ___)
B' (___, ___)
C' (___, ___)
Tip: Subtract 3 from x, add 4 to y, then plot the new vertices above.
Turn page over to complete independent practice. Middle School Geometry • Rigid Transformations
Independent Practice Coordinate Transformations
Translations on Your Own
Page: 2 of 2
Check each vertex shift carefully
Problem 5 Identify Translation
How many units has \(\Delta ABC\) been translated to form \(\Delta A'B'C'\)?
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C A' B' C'
Vertices
A (-2, 5) → A' (-1, -1)
B (1, 5) → B' (2, -1)
C (-2, 2) → C' (-1, -4)
Translation:
Coordinate Rule: \((x, y) \to (\) , \()\)
How do the new ordered pairs relate to the original?
Problem 6 Identify Translation
How many units has \(\Delta ABC\) been translated to form \(\Delta A'B'C'\)?
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C A' B' C'
Vertices
A (0, -2) → A' (-4, 6)
B (4, -2) → B' (0, 6)
C (0, -5) → C' (-4, 3)
Translation:
Coordinate Rule: \((x, y) \to (\) , \()\)
How do the new ordered pairs relate to the original?
Problem 7 Graph Translation
Translate the figure 4 units up. Graph and label \(\Delta A'B'C'\).
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C
Original Vertices
A (0, -2)
B (2, -5)
C (-2, -5)
Coordinate Rule:
\((x, y) \to (x, y+4)\)
New Image Coordinates:
A' (___, ___)
B' (___, ___)
C' (___, ___)
Tip: Add 4 to each y-coordinate, then plot the new vertices on the grid above.
Problem 8 Graph Translation
Translate the figure 3 units right and 6 units down. Graph \(\Delta A'B'C'\).
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6 A B C
Original Vertices
A (-2, 6)
B (0, 3)
C (-4, 3)
Coordinate Rule:
\((x, y) \to (x+3, y-6)\)
New Image Coordinates:
A' (___, ___)
B' (___, ___)
C' (___, ___)
Tip: Add 3 to x, subtract 6 from y, then plot the new vertices above.
Rule Mastery Quick Check
Point \(P(-5, 8)\) is translated by rule \((x, y) \to (x + 7, y - 9)\). What are the coordinates of \(P'\)?
\(P' =\) (___, ___)
A triangle is shifted 5 units left and 2 units down. Write the algebraic translation rule:
\((x, y) \to\) (___, ___)
Be sure all vertices and labels are accurately plotted on each coordinate grid! Translations Practice • Page 2 of 2
Grid Gliders Answer Key
Teacher Answer Key Coordinate Transformations
Grid Gliders: Translations — Key
Course: Grade 8 Geometry
Page: 1 of 2
Key Takeaway: Translations preserve size, shape, and angle measures (isometry / rigid motion).
Rule: \((x, y) \to (x + a, y + b)\)
Problem 1 Solution Horizontal Shift
How many units has the object been translated and in what direction?
x y -6 -2 2 6 A B C A' B' C' 6 units left
Vertices
A (1, 4) → A' (-5, 4)
B (4, 0) → B' (-2, 0)
C (1, 0) → C' (-5, 0)
Translation: 6 units left
Coordinate Rule: \((x, y) \to (x - 6, y)\)
Coordinate Relationship:
Each x-coordinate decreases by 6 (\(x - 6\)). The y-coordinates remain unchanged.
Problem 2 Solution Diagonal Shift
How many units has the object been translated and in what direction?
x y -6 -2 2 6 A B C A' B' C'
Vertices
A (-3, 5) → A' (0, -2)
B (0, 1) → B' (3, -6)
C (-3, 1) → C' (0, -6)
Translation: 3 units right and 7 units down
Coordinate Rule: \((x, y) \to (x + 3, y - 7)\)
Coordinate Relationship:
Add 3 to each x-coordinate (\(x+3\)); subtract 7 from each y-coordinate (\(y-7\)).
Problem 3 Solution Graphed Image
Translate the figure 4 units to the right.
x y A B C A'(1,5) B'(2,1) C'(0,1)
Transformations
A (-3, 5) → A'(1, 5)
B (-2, 1) → B'(2, 1)
C (-4, 1) → C'(0, 1)
Rule: \((x+4, y)\)
Correct Output Coordinates:
A' (1, 5) B' (2, 1) C' (0, 1)
Problem 4 Solution Graphed Image
Translate the figure 3 units left and 4 units up.
x y A B C A'(-1,3) B'(0,0) C'(-2,0)
Transformations
A (2, -1) → A'(-1, 3)
B (3, -4) → B'(0, 0)
C (1, -4) → C'(-2, 0)
Rule: \((x-3, y+4)\)
Correct Output Coordinates:
A' (-1, 3) B' (0, 0) C' (-2, 0)
Teaching Tip: Remind students that rigid transformations do not distort side lengths or angle measures. Translations Key • Page 1 of 2
Teacher Answer Key Coordinate Transformations
Independent Practice — Key
Page: 2 of 2
Full worked solutions
Problem 5 Solution 1 Right, 6 Down
How many units has \(\Delta ABC\) been translated to form \(\Delta A'B'C'\)?
