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Solved Examples and Worksheet for Transformations-Reflections

Q1Identify the coordinates of the image of the point K3,6 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 K3,6.
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 theverticalline and the reflected figure is the same as the original figure.
Step: 3
So, the transformation illustrated in the figure is reflection.
Correct Answer 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
ΔABD and ΔADC are congruent
  [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 P2,4, 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 P2,4 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 P2,4 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 P5,8 in x-axis is 5,8
Correct Answer is :   5,8