You’ve uploaded a worksheet titled
“Translations” that asks you to perform geometric translations on shapes drawn on coordinate grids. A
translation is a type of transformation that slides a shape without rotating or resizing it — every point of the shape moves the same distance in the same direction.
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Let’s go problem by problem and explain how to solve each one.
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Problem 1: Translation: 3 right
-
Original Shape: A green triangle with vertices at approximately:
- (-4, -1)
- (-4, -4)
- (-2, -4)
-
Translation Rule: Move every point
3 units to the right → add 3 to each x-coordinate.
-
New Coordinates:
- (-4 + 3, -1) =
(-1, -1)
- (-4 + 3, -4) =
(-1, -4)
- (-2 + 3, -4) =
(1, -4)
✔ Draw the triangle with vertices at (-1, -1), (-1, -4), (1, -4)
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Problem 2: Translation: 2 right and 3 down
-
Original Shape: A green trapezoid with vertices at approximately:
- (-3, 2)
- (-2, 2)
- (-1, 1)
- (-3, 1)
-
Translation Rule: Add 2 to x (right), subtract 3 from y (down).
-
New Coordinates:
- (-3+2, 2-3) =
(-1, -1)
- (-2+2, 2-3) =
(0, -1)
- (-1+2, 1-3) =
(1, -2)
- (-3+2, 1-3) =
(-1, -2)
✔ Draw the trapezoid with vertices at (-1,-1), (0,-1), (1,-2), (-1,-2)
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Problem 3: Translation: 5 left
-
Original Shape: A green triangle with vertices at approximately:
- (2, -1)
- (4, -1)
- (4, -3)
-
Translation Rule: Subtract 5 from each x-coordinate.
-
New Coordinates:
- (2-5, -1) =
(-3, -1)
- (4-5, -1) =
(-1, -1)
- (4-5, -3) =
(-1, -3)
✔ Draw the triangle with vertices at (-3,-1), (-1,-1), (-1,-3)
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Problem 4: Translation: 4 left and 3 down
-
Original Shape: A green “stair-step” shape with vertices at approximately:
- (1, 3)
- (2, 3)
- (2, 2)
- (3, 2)
- (3, 1)
- (2, 1)
- (2, 0)
- (1, 0)
*(Note: This is a connected path — trace all points)*
-
Translation Rule: Subtract 4 from x, subtract 3 from y.
-
New Coordinates:
- (1-4, 3-3) =
(-3, 0)
- (2-4, 3-3) =
(-2, 0)
- (2-4, 2-3) =
(-2, -1)
- (3-4, 2-3) =
(-1, -1)
- (3-4, 1-3) =
(-1, -2)
- (2-4, 1-3) =
(-2, -2)
- (2-4, 0-3) =
(-2, -3)
- (1-4, 0-3) =
(-3, -3)
✔ Plot these points in order and connect them to form the translated shape.
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Problem 5: Translation: 4 left and 5 down
-
Original Shape: A green quadrilateral with vertices at approximately:
- (1, 2)
- (3, 2)
- (3, 1)
- (2, 0)
-
Translation Rule: Subtract 4 from x, subtract 5 from y.
-
New Coordinates:
- (1-4, 2-5) =
(-3, -3)
- (3-4, 2-5) =
(-1, -3)
- (3-4, 1-5) =
(-1, -4)
- (2-4, 0-5) =
(-2, -5)
✔ Draw the quadrilateral with these new vertices.
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Problem 6: Translation: 3 right and 4 up
-
Original Shape: A green triangle with vertices at approximately:
- (-3, -2)
- (-1, -2)
- (-2, -4)
-
Translation Rule: Add 3 to x, add 4 to y.
-
New Coordinates:
- (-3+3, -2+4) =
(0, 2)
- (-1+3, -2+4) =
(2, 2)
- (-2+3, -4+4) =
(1, 0)
✔ Draw the triangle with vertices at (0,2), (2,2), (1,0)
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✔ Final Tips:
- Always pick
key points (vertices) of the shape.
- Apply the translation rule to
each point.
- Plot the new points and
connect them in the same order as the original.
- Double-check your math — especially signs (left = minus x, down = minus y).
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If you’re submitting this as homework, just draw the translated shapes accurately on the grids using the new coordinates we calculated above.
Let me know if you’d like me to generate a visual version or printable answer key! 🖍️📐
Parent Tip: Review the logic above to help your child master the concept of translation worksheet pdf.
