Question

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Part 2: Graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the preimage and image using the correct notation.

4. A(2, 1), B(3, -1), C(4, 2), D(3, 3)
Reflection : in the line x = -1

5. A(2, 3), B(1, 4), C(3, 4)
Rotation: 180° about the origin

6. A(5, -2), B(5, 2), C(3, 1), D(2, -1)
Rotation: 270° about the origin

Answer 1

Question 4:

• A' (-4, 1)
• B' (-4, -1)
• C' (-6, 2)
• D' (-5, 3)

Question 5:

• A' (-2, -3)
• B' (-1, -4)
• C' (-3, -4)

Question 6:

• A' (-2, -5)
• B' (2, -5)
• C' (1, -3)
• D' (-1, -2)

Explanation:

Question 4

Given vertices of the pre-image:

• A = (2, 1)
• B = (2, -1)
• C = (4, 2)
• D = (3, 3)

If the pre-image is reflected in the line x = -1, the transformation rule is:

• 
  `(x, y) \rightarrow (x-2(x+1), y)`

Therefore the vertices of the image are:

• A' = (2 - 2(2 + 1), 1) = (-4, 1)
• B' = (2 - 2(2 + 1), -1) = (-4, -1)
• C' = (4 - 2(2 + 1), 2) = (-6, 2)
• D' = (3 - 2(2 + 1), 3) = (-5, 3)

Question 5

Given vertices of the pre-image:

• A = (2, 3)
• B = (1, 4)
• C = (3, 4)

If the pre-image is rotated 180° about the origin, the transformation rule is:

• 
  `(x, y) \rightarrow (-x,-y)`

Therefore the vertices of the image are:

• A' = (-2, -3)
• B' = (-1, -4)
• C' = (-3, -4)

Question 6

Given vertices of the pre-image:

• A = (5, -2)
• B = (5, 2)
• C = (3, 1)
• D = (2, -1)

If the pre-image is rotated 270° about the origin, the transformation rule is:

• 
  `(x, y) \rightarrow (y,-x)`

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

• A' = (-2, -5)
• B' = (2, -5)
• C' = (1, -3)
• D' = (-1, -2)