Math 2 Final Exam Review

If triangle DEF is reflected over the line y = x, and D is (5, -2) what is the coordinate of D'?

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Answer explanation

To reflect point D(5, -2) over the line y = x, swap the x and y coordinates. Thus, D' becomes (-2, 5).

What is the arrow rule for a dilation with scale factor 4?

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Answer explanation

The arrow rule for a dilation with scale factor 4 states that if you have a point A and its image A' after dilation, the distance from the center of dilation to A' is 4 times the distance from the center to A.

If rectangle ABCD is rotated 90° clockwise about point B, what are the coordinates of the image of point C?

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Answer explanation

Rotating point C 90° clockwise around point B means moving it to the position where it was originally to the left of B. If B is at (x,y) and C is at (x+a,y+b), the new coordinates of C will be (x-b,y+a).

Given the original point (x, y) write the transformation rule for the translation “5 left, 4 down.”

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Answer explanation

To translate the point (x, y) "5 left, 4 down," subtract 5 from x and 4 from y. The transformation rule is (x, y) -> (x - 5, y - 4).

Triangle ABC is dilated with the center at the origin to form triangle A’B’C’. What is the scale factor of the dilation if A is (2, 3) and A’ is (8, 12)?

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Answer explanation

To find the scale factor, divide the coordinates of A' by A. For A(2, 3) and A'(8, 12), the scale factor is 8/2 = 4 and 12/3 = 4. Thus, the scale factor of the dilation is 4.

Look at rectangle ABCD. What are the coordinates of the image of point D after 180° clockwise rotation about A?

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Answer explanation

To rotate point D 180° clockwise about point A, you reflect D across A. If D has coordinates (x,y), the new coordinates after rotation will be (2a-x, 2b-y), where A is (a,b). Calculate to find the new position.

Which transformation(s) always preserve the dimensions of a figure?

• Translation

• Dilation

• Reflection

• Rotation

Answer explanation

Translation, reflection, and rotation preserve the dimensions of a figure by maintaining its size and shape. Dilation, however, changes the size of the figure, so it does not preserve dimensions.

Triangle ABC is dilated with the center at the origin to form triangle A’B’C’. What is the scale factor of the dilation if A is (10, 4) and A’ is (5, 2)?

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Answer explanation

To find the scale factor, divide the coordinates of A' by A. For A (10, 4) and A' (5, 2), the scale factor is 5/10 = 1/2 for x and 2/4 = 1/2 for y. Thus, the scale factor of the dilation is 1/2.

Which of the following figures have both line and rotational symmetry?

• A

• B

• C

• D

Answer explanation

Figure D has both line symmetry (it can be folded along a line and match) and rotational symmetry (it looks the same after a rotation). The other figures lack one or both types of symmetry.

Which of the following transformations will map △ABC onto △DEF?

• Reflect △ABC over the y-axis and shift up 6 spaces.

• Reflect △ABC over the x-axis and shift 6 spaces.

• Reflect △ABC over the y-axis and shift down 6 spaces.

• Reflect △ABC over the y-axis, reflect over the x-axis, and shift down 4 spaces.

Answer explanation

Reflecting △ABC over the y-axis reverses its x-coordinates, and shifting up 6 spaces moves it vertically. This combination correctly positions △ABC to match △DEF, making it the correct transformation.