Question

name: 15. what type of symmetry does the following picture represent? a translational symmetry b rotational symmetry c reflection symmetry d none of the above directions (16 - 17): describe each figures rotational symmetry. 16. 17. the darker shape is the original shape a 90° clockwise rotations b 90° counter - clockwise rotations c ¼ clockwise rotations d all of the above a 270° counter - clockwise b 90° clockwise c ¼ clockwise d all of the above 18. translate the figure according to the arrow. 19. translate the figure left 5 spaces and up 7 spaces. 20. which rule correctly describes the translation shown on the graph? a (x,y)→(x + 3,y - 4) b (x,y)→(x + 3,y + 4) c (x,y)→(x - 3,y - 4) d (x,y)→(x - 3,y + 4) 21. translate the triangle (x - 7,y + 6).

Explanation:

Step1: Analyze question 15

The given shape has no line of symmetry (so not reflection symmetry), no repeating pattern for translational symmetry, and no angle of rotation (other than 360°) that maps it onto itself. So it has none of the given symmetries.

Step2: Analyze question 16

The figure looks the same after 90° clock - wise, 90° counter - clockwise and 1/4 (which is 90°) clockwise rotations. So all of these rotations describe its rotational symmetry.

Step3: Analyze question 17

The figure does not have rotational symmetry as described in the options. But if we consider the general concept, it has no regular rotational symmetry as it doesn't map onto itself at common rotation angles like 90°, 180°, 270°.

Step4: Analyze question 18

To translate the figure according to the arrow, we move each point of the triangle in the direction of the arrow.

Step5: Analyze question 19

To translate the figure left 5 spaces and up 7 spaces, we subtract 5 from the x - coordinates and add 7 to the y - coordinates of each point of the figure.

Step6: Analyze question 20

By observing the movement of the points of the triangle in the graph, we can see that the x - coordinate increases by 3 and the y - coordinate decreases by 4. So the rule is $(x,y)\to(x + 3,y-4)$.

Step7: Analyze question 21

To translate the triangle using the rule $(x - 7,y + 6)$, we subtract 7 from the x - coordinates and add 6 to the y - coordinates of each vertex of the triangle.

Answer:

1. D. None of the above
2. D. All of the above
3. (No correct option as the figure has no regular rotational symmetry as in options)
4. (Requires drawing the translated figure by moving points in arrow direction)
5. (Requires drawing the translated figure by adjusting x and y coordinates of points)
6. A. $(x,y)\to(x + 3,y-4)$
7. (Requires drawing the translated triangle by adjusting x and y coordinates of vertices)