SAT Practice Test For Geometry Transformations

1.

What two transformations were performed to obtain /\ X"Y"Z" in the diagram?

Reflection, reflection

Reflection, rotation

Reflection, translation

Translation, reflection

Rotation, reflection

The correct answer is reflection, reflection. This means that the shape was reflected twice to obtain /\ X"Y"Z".

Explanation

The correct answer is reflection, reflection. This means that the shape was reflected twice to obtain /\ X"Y"Z".

2. Which of the following is not a rotation of this figure?

A

B

C

D

E

not-available-via-ai

Explanation

not-available-via-ai

3. How many lines of symmetry does the polygon at the right have?

2

10

4

8

6

The polygon at the right has 8 lines of symmetry. A line of symmetry is a line that divides a shape into two equal halves, where each half is a mirror image of the other. By examining the polygon, we can see that there are 8 different lines that can be drawn to divide it into two equal halves. Therefore, the correct answer is 8.

Explanation

The polygon at the right has 8 lines of symmetry. A line of symmetry is a line that divides a shape into two equal halves, where each half is a mirror image of the other. By examining the polygon, we can see that there are 8 different lines that can be drawn to divide it into two equal halves. Therefore, the correct answer is 8.

4. What type of transformation is shown in the diagram.

Slide

Translation

Reflection

Rotation

Isometry

The correct answer is reflection. In a reflection, an object is flipped over a line called the line of reflection. The diagram likely shows an object that has been flipped over a line, creating a mirror image of itself. This type of transformation is called a reflection.

Explanation

The correct answer is reflection. In a reflection, an object is flipped over a line called the line of reflection. The diagram likely shows an object that has been flipped over a line, creating a mirror image of itself. This type of transformation is called a reflection.

5.

The point P(-3, 7) is reflected in the line y=x. What are the coordinates of P'?

(-3, -7)

(3, -7)

(3, 7)

(-7, 3)

None of these

When a point is reflected in the line y=x, the x-coordinate and y-coordinate of the point are swapped. In this case, the x-coordinate of P is -3 and the y-coordinate is 7. When they are swapped, the new x-coordinate becomes 7 and the new y-coordinate becomes -3. Therefore, the coordinates of P' are (7, -3).

Explanation

When a point is reflected in the line y=x, the x-coordinate and y-coordinate of the point are swapped. In this case, the x-coordinate of P is -3 and the y-coordinate is 7. When they are swapped, the new x-coordinate becomes 7 and the new y-coordinate becomes -3. Therefore, the coordinates of P' are (7, -3).

6. How many lines of symmetry does the infield of a baseball field have?

0

1

2

3

4

The infield of a baseball field has one line of symmetry. This means that if you were to fold the infield in half along this line, both halves would match perfectly. The other options, 0, 2, 3, and 4, are incorrect because they do not accurately represent the number of lines of symmetry in the infield of a baseball field.

Explanation

The infield of a baseball field has one line of symmetry. This means that if you were to fold the infield in half along this line, both halves would match perfectly. The other options, 0, 2, 3, and 4, are incorrect because they do not accurately represent the number of lines of symmetry in the infield of a baseball field.