#### Solved Examples and Worksheet for Transformations-Reflections

Q1Identify the coordinates of the image of the point K(- 3, 6) after reflection over the y-axis.

A. (3, - 6)
B. (3, 6)
C. (- 3, 6)
D. (- 3, - 6)

Step: 1
Reflection is the mirror image formed when the point is flipped over the line of reflection.
Step: 2
Plot the point K(- 3, 6).
Step: 3
As the point (- 3, 6) is flipped over the y-axis, the y-coordinate remains the same and the x-coordinate will be 3.
Step: 4
So, the coordinates of the image are K′(3, 6).
Correct Answer is :   (3, 6)
Q2Name the transformation illustrated in the figure.

A. reflection
B. translation
C. rotation
D. rotation and reflection

Step: 1
A reflection flips a figure over a line of reflection. The reflected figure, or image, is the same as the original figure.
Step: 2
From the figure, it is clear that the figure is flipped over a line of reflection (the vertical line) and the reflected figure is the same as the original figure.
Step: 3
So, the transformation illustrated in the figure is reflection.
Q3ΔPQR is the reflection image of ΔABC as shown. Find the values of x and y.
[Given PQ = y + 2, AB = 6, BC = 2x - 2 and QR = 8.]

A. x = 5, y = 5
B. x = 4, y = 4
C. x = 5, y = 4
D. x = 6, y = 4

Step: 1
From the figure, PQ¯ is the reflection image of AB¯. So, y + 2 = 6 y = 4.
[Solve for y.]
Step: 2
From the figure, RQ¯ is the reflection image of CB¯. So, 2x - 2 = 8 x = 5.
[Solve for x.]
Correct Answer is :   x = 5, y = 4
Q4ΔABC is equilateral, D is the mid point of BC¯ as shown. What is the area of ΔABD if the area of ΔADC is 2.3 cm2?

A. 2.3 cm2
B. 4.6 cm2
C. 5.3 cm2
D. 3.3 cm2

Step: 1
ΔABC is an equilateral triangle in which D is the mid point of BC¯. From the figure, AD¯ is median through A to BC¯.
Step: 2
Since medians are the perpendicular bisectors of the sides in an equilateral triangle, line l is the perpendicular bisector of BC¯.
Step: 3
So, the reflection of ΔABD in line l is ΔADC
[Steps 1, 2.]
Step: 4
[Reflection is an isometry.]
Step: 5
So, area of ΔABD = area of ΔADC = 2.3 cm2
[Reflection does not change area.]
Correct Answer is :   2.3 cm2
Q5What are the coordinates of the image of (x, y) when it is reflected onto the y-axis?

A. (x, -y)
B. (x, y)
C. (-x, y)
D. (-x, -y)

Step: 1
Given point is (x, y) and the line of reflection is y-axis, y-axis is the perpendicular bisector of the line segment joining (x, y) and (-x, y) .
Step: 2
So, the reflection image of P(x, y) in the y-axis is (-x, y) .
Correct Answer is :   (-x, y)
Q6The coordinates of point A of the triangle ABC are (- 2, 2). If the triangle is reflected on X-axis, what are the coordinates of A′ ?

A. (- 2, - 2)
B. (2, 2)
C. (3, 2)
D. (2, - 2)

Step: 1
Since the triangle is reflected on the x-axis, the x-coordinate will not change.
Step: 2
Since A is 2 units up from the x-axis, the reflected point will be 2 units down from the x-axis.
Step: 3
The coordinates of point A′ are (-2 , -2)
Correct Answer is :   (- 2, - 2)
Q7The coordinates of point A of the triangle ABC are (- 2, 4). What are the coordinates of A′, if the triangle is reflected on x-axis?

A. (2, 4)
B. (- 2, - 4)
C. (3, 2)
D. None of the above

Step: 1
Since the triangle is reflected on the x-axis, the x-coordinate will not change.
Step: 2
Since A is 4 units up from the x-axis, the reflected point will be 4 units down from the x-axis.
Step: 3
The coordinates of point A′ are (-2, -4).
Correct Answer is :   (- 2, - 4)
Q8The point C (4, - 3) is first reflected over x-axis and then reflected over y-axis. What are the coordinates of the final image?
A. (4, 3)
B. (- 4, 3)
C. (4, - 3)
D. (3, - 4)

Step: 1
When a point is reflected over a horizontal line, the x-coordinate remains the same and the sign of the y-coordinate changes.
Step: 2
The coordinates of the point after the reflection on x-axis is (4, 3).
Step: 3
When a point is reflected over a vertical line, the y-coordinate remains the same and the sign of the x-coordinate changes.
Step: 4
The coordinate of the point when reflected over the y-axis is (- 4, 3) as shown in the following figure.
Step: 5
The coordinates of the final image of point C' are (- 4, 3).
Correct Answer is :   (- 4, 3)
Q9What are the coordinates of the point P(-2, -4), when reflected over the line x = 3?
A. (5, 4)
B. (-5, 4)
C. (8, -4)
D. None of the above

Step: 1
When a point is reflected over a vertical line the y-coordinate remains the same.
Step: 2
The point P(-2, -4) is reflected over the line x = 3.
Step: 3
The distance of the point from the line x = 3 is 2 + 3 = 5.
Step: 4
So, the image of the point will be 5 units away from the line x = 3.
Step: 5
The x-coordinate of the image of the point with respect to the coordinate axes = 5 + 3 = 8.
Step: 6
So, the coordinates of the image of the point P(-2, -4) along x = 3 are (8, -4).
Correct Answer is :   (8, -4)
Q10What are the coordinates of the point P (- 5, - 8) when reflected over x-axis?
A. (5, 8)
B. (5, - 8)
C. (- 5, 8)
D. (- 5, - 8)

Step: 1
To find the image of any point P(a, b) in the x-axis, keep the x-coordinate same and change the sign of the y-coordinate.
Step: 2
So, the image of the point P(- 5, - 8) in x-axis is (- 5, 8)
Correct Answer is :   (- 5, 8)