Transformations and Similarity Quiz

• Translation

• Reflection over the x-axis

• Rotation

• Dilation

Answer explanation

The original triangle's vertices are reflected over the x-axis to obtain the new vertices. This is evident as the y-coordinates change signs while the x-coordinates remain the same, confirming the transformation is a reflection over the x-axis.

Answer explanation

A 90-degree clockwise rotation transforms the point (x, y) to (y, -x). For (3, 4), this results in (4, -3), which is the correct answer.

Answer explanation

To find the image of the vertex (4, 3) after dilation by a scale factor of 2, multiply both coordinates by 2: (4*2, 3*2) = (8, 6). Thus, the correct answer is (8, 6).

Two triangles are similar, and the sides of the first triangle are 3, 4, and 5. If the longest side of the second triangle is 10, what is the length of the shortest side of the second triangle?

• 6

• 7.5

• 5

• 4

Answer explanation

The triangles are similar, so the ratio of corresponding sides is constant. The longest side of the first triangle is 5, and the longest side of the second triangle is 10. The ratio is 10/5 = 2. The shortest side of the first triangle is 3, so the shortest side of the second triangle is 3 * 2 = 6.

Answer explanation

When a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. The vertex (2, 3) reflects to (-2, 3), making the correct answer (-2, 3).

Answer explanation

To find the new point after translation, add the vector (3, -2) to the point (-1, 4). This gives: (-1 + 3, 4 - 2) = (2, 2). Thus, the correct answer is (2, 2).

• 1

• 2

• 3

• 0.5

Answer explanation

To find the scale factor, compare the coordinates of the original triangle and the dilated triangle. Each vertex of the dilated triangle is twice the corresponding vertex of the original triangle, confirming a scale factor of 2.

In a pair of similar triangles, the sides of one triangle are 5, 12, and 13. If the shortest side of the other triangle is 10, what is the length of the longest side of this triangle?

• 20

• 24

• 26

• 30

Answer explanation

The triangles are similar, so the ratio of corresponding sides is constant. The shortest side of the first triangle is 5, and the shortest side of the second triangle is 10, giving a ratio of 10/5 = 2. The longest side of the first triangle is 13, so the longest side of the second triangle is 13 * 2 = 26.

• Rotation 180 degrees

• Reflection over the y-axis

• Translation

• Dilation

Answer explanation

The point (3, 5) is transformed to (-3, 5) by reflecting it over the y-axis. This changes the x-coordinate from 3 to -3 while keeping the y-coordinate the same, confirming that the correct transformation is reflection over the y-axis.

Answer explanation

Reflecting the point (4, 7) over the line y = x swaps its coordinates. Thus, (4, 7) becomes (7, 4), which is the correct answer.