Write the New Coordinates worksheet for practicing graphing transformations on a coordinate plane.

Let’s go through each problem step by step.

We are given a shape (a quadrilateral) on a coordinate grid, and we need to translate it (move it) according to the instructions, then write the new coordinates of the four points: C, D, E, F.

First, let’s find the original coordinates of the points from the graph in Problem 1:

Looking at the first graph (Problem 1):

- Point C is at (4, 5)
- Point D is at (3, 2)
- Point E is at (1, 3)
- Point F is at (2, 6)

Translation instruction for Problem 1: “1 unit down and 1 unit left”

That means:
- Subtract 1 from the x-coordinate (left)
- Subtract 1 from the y-coordinate (down)

So:

C' = (4 - 1, 5 - 1) = (3, 4)
D' = (3 - 1, 2 - 1) = (2, 1)
E' = (1 - 1, 3 - 1) = (0, 2)
F' = (2 - 1, 6 - 1) = (1, 5)

✔ Check: All subtractions correct.

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Problem 2: “2 units right and 1 unit up”

Original points (same as above):

C(4,5), D(3,2), E(1,3), F(2,6)

Add 2 to x (right), add 1 to y (up):

C' = (4+2, 5+1) = (6, 6)
D' = (3+2, 2+1) = (5, 3)
E' = (1+2, 3+1) = (3, 4)
F' = (2+2, 6+1) = (4, 7)

✔ Check: All additions correct.

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Problem 3: “4 units up and 5 units left”

Original points again:

C(4,5), D(3,2), E(1,3), F(2,6)

Subtract 5 from x (left), add 4 to y (up):

C' = (4-5, 5+4) = (-1, 9)
D' = (3-5, 2+4) = (-2, 6)
E' = (1-5, 3+4) = (-4, 7)
F' = (2-5, 6+4) = (-3, 10)

✔ Check: All calculations correct.

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Problem 4: “4 units left and 5 units down”

Original points:

C(4,5), D(3,2), E(1,3), F(2,6)

Subtract 5 from y (down), subtract 4 from x (left):

C' = (4-4, 5-5) = (0, 0)
D' = (3-4, 2-5) = (-1, -3)
E' = (1-4, 3-5) = (-3, -2)
F' = (2-4, 6-5) = (-2, 1)

✔ Check: All correct.

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Problem 5: “7 units right”

Only move right — add 7 to x, y stays same.

C' = (4+7, 5) = (11, 5)
D' = (3+7, 2) = (10, 2)
E' = (1+7, 3) = (8, 3)
F' = (2+7, 6) = (9, 6)

✔ Check: Correct.

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Problem 6: “6 units down and 6 units left”

Subtract 6 from x and y.

C' = (4-6, 5-6) = (-2, -1)
D' = (3-6, 2-6) = (-3, -4)
E' = (1-6, 3-6) = (-5, -3)
F' = (2-6, 6-6) = (-4, 0)

✔ Check: All correct.

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Final Answer:

1) C'(3,4), D'(2,1), E'(0,2), F'(1,5)
2) C'(6,6), D'(5,3), E'(3,4), F'(4,7)
3) C'(-1,9), D'(-2,6), E'(-4,7), F'(-3,10)
4) C'(0,0), D'(-1,-3), E'(-3,-2), F'(-2,1)
5) C'(11,5), D'(10,2), E'(8,3), F'(9,6)
6) C'(-2,-1), D'(-3,-4), E'(-5,-3), F'(-4,0)