# Translation Rotation Reflection Worksheet - Page 2

Translation Rotation Reflection Worksheet
• Page 2
11.
The point (3, -4) is first reflected over Y-axis and then reflected over X-axis. What are the coordinates of the final image?
 a. (4, -3) b. (3, 4) c. (-3, 4) d. None of the above

#### Solution:

When a point is reflected over a vertical line, the y-coordinate remains the same and the sign of the x-coordinate changes.

So, the coordinate of the point when reflected over the Y-axis is (-3, -4).

When a point is reflected over a horizontal line, the x-coordinate remains the same and the sign of the y-coordinate changes.

So, the coordinates of the point after the reflection on X-axis is (-3, 4).

12.
Does an equilateral triangle have rotational symmetry? If yes, what is the angle of rotation?
 a. Yes, 90o b. No c. Yes, 180o d. Yes, 120o

#### Solution:

A figure has rotational symmetry, if the image after a rotation of 180o or less fits exactly on top of the original figure.

If an equilateral triangle is rotated to 120o, the new image exactly fits on the original triangle.

So, an equilateral triangle has rotational symmetry and the angle of rotation is 120o.

13.
What is the translation of the rectangle shown in the figure, if the coordinates of K and K1 are (-5, 1) and (-3, -3)?

 a. Horizontal 4 and vertical -2 b. Horizontal 2 and vertical 4 c. Horizontal 2 and vertical -4 d. None of the above

#### Solution:

The coordinates of K and K1 are (-5, 1) and (-3, -3).

Horizontal translation = -3 - (-5) = -3 + 5 = 2 units.

Vertical translation = -3 -1 = -4 units.

14.
If the coordinates of a point are (-3, 5) and after translation the coordinates are (3, 5), then what is the translation?
 a. 6 units right b. 6 units left c. 3 units right d. None of the above

#### Solution:

The coordinates before translation and after translation are (-3, 5) and (3, 5) respectively.

The x-coordinate after translation is greater than that before translation but the y-coordinate is not changed. So, the translation is towards right.

Translation = 3 - (-3) = 3 + 3 = 6 units right.

15.
The coordinates of a line segment are (3, 2) and (1, -4). What are the new coordinates of the line segment, if it is translated 3 units left?
 a. (0, 2) and (-2, -4) b. (0, 2) and (-2, 4) c. (0, -2) and (-2, -4) d. None of the above

#### Solution:

The coordinates of the line segment are (3, 2) and (1, -4), respectively.

The translation is done by 3 units left.

Since, the translation is done to left, the y-coordinate does not change.

3 - 3 = 0 and 1 - 3 = -2.
[x-coordinates of each end point gets reduced by 5.]

The new coordinates of the line segment are (0, 2) and (-2, -4).

16.
After translation of the point D (3, 4), the new coordinates are D1 (7, 4). What is the translation?
 a. 4 units left b. 4 units right c. 4 units up d. None of the above

#### Solution:

The two points are (3, 4) and (7, 4).

As the y-coordinate is not changing and the x-coordinate is positive and increasing, the translation is towards right.

The translation of the point is 7 - 3 = 4 units to the right.

17.
The coordinates of point A of the triangle ABC are (-4, 4). If the triangle is reflected on X-axis, what are the coordinates of A1?

 a. (3, 4) b. (4, 4) c. (-4, -4) d. None of the above

#### Solution:

Since the triangle is reflected on the x-axis, the x-coordinate will not change.

Since A is 4 units up from the x-axis, the reflected point will be 4 units down from the x-axis.

The coordinates of point A1 are (-4, -4).

18.
What would be the image of a polygon reflected over a line with respect to the original polygon?
 a. Similar b. Congruent c. Increase in size d. None of the above

#### Solution:

A reflection flips the figure across a line. The new figure is a mirror image of the original figure.

So, the image of the polygon reflected over a line is congruent with respect to the original polygon.

19.
What are the coordinates of the point P(-5, -7), when reflected over the line $x$ = 5?
 a. (15, -7) b. (-10, 7) c. (10, 7) d. None of the above

#### Solution:

When a point is reflected over a vertical line the y-coordinate remains the same.

The point P(-5, -7) is reflected over the line x = 5.

The distance of the point from the line x = 5 is 5 + 5 = 10.

So, the image of the point will be 10 units away from the line x = 5.

The x-coordinate of the image of the point with respect to the coordinate axes = 10 + 5 = 15.

So, the coordinates of the image of the point P(-5, -7) along x = 5 are (15, -7).

20.
When corresponding points of an original figure and its reflection are connected, the resultant segments will be _________ to the line of reflection.
 a. Parallel b. Perpendicular

#### Solution:

The original figure and its reflection will be on either sides of the line of reflection and will be like mirror images.

So, the resulting segments will be perpendicular to the line of reflection.