﻿?> Reflection Worksheet | Problems & Solutions

# Reflection Worksheet

Reflection Worksheet
• Page 1
1.
How many lines of symmetry does the figure shown contain?

 a. 1 b. 3 c. 2

#### Solution:

We do not get two similar figures by folding the shown figure through any line. So there is no line of symmetry for the figure shown.

2.
Name the transformation shown.

 a. turn b. rotation c. reflection d. translation

#### Solution:

In the figure, ABCD has clockwise orientation and its image A′B′C′D′ has counter clockwise orientation.

The line m bisects AA′, BB′, CC′ and DD′ perpendicularly. So, from the definition of reflection, the shown transformation is a reflection.

3.
Which of the following is the reflection image of the given figure in the line shown?

 a. Figure - 1 b. Figure - 4 c. Figure - 2 d. Figure - 3

#### Solution:

Figure - 1 shows the reflection image of the given figure in the given line.

4.
If the point M(5, - 4) is reflected in the line $y$ = - 1, then find the coordinates of the reflected image of M.
 a. (5, - 5) b. (5, 2) c. (5, 4) d. (3, - 6)

#### Solution:

Locate the point M(5, - 4) on coordinate plane.

Reflect the point M with respect to the line y = - 1

The image of point M after reflection is (5, 2).

5.
ΔE′C′D′ is the reflection image of ΔECD under the line $l$ as shown. Then ED = ___.

 a. E′D′ b. C′E′ c. CD d. EC

#### Solution:

Since ΔE′C′D′ is the reflection image of ΔECD under the line l, ΔE′C′D′ ΔECD. So, ED E′D′ and hence ED = E′D′

6.
Name the transformation shown.

 a. rotation b. reflection c. translation

#### Solution:

In the figure, ABCD has clockwise orientation and its image A′B′C′D′ has counterclockwise orientation..

The line L bisects AA′, BB′, CC′ and DD′ perpendicularly. So, from the definition of reflection, the shown transformation is a reflection.

7.
Which of the following is not correct?
 a. A reflection reverses orientation b. A reflection does not reverse orientation c. A reflection does not change size d. A reflection is an isometry

#### Solution:

A reflection is an isometry, which does not change the size of the figures. Reflection reverses orientation of the figures.
[By definition.]

8.
ΔABC is isosceles, D is the midpoint of side $\stackrel{‾}{\mathrm{BC}}$ as shown. What is the reflection image of C under the line $l$?

 a. B b. D c. A d. C itself

#### Solution:

ΔABC is an isosceles triangle in which D is the mid point of the side BC and AB = AC.
[From the figure .]

From the figure AD is median through A to side BC.

Since, in an isosceles triangle the median through vertex is the perpendicular bisector of its base, line l is the perpendicular bisector of side BC.

So, the reflection image of C in the line l is B.

9.
What is the reflection image of $\stackrel{‾}{\mathrm{MN}}$ in the $x$-axis?

 a. $\stackrel{‾}{\mathrm{MN}}$ b. $\stackrel{‾}{\mathrm{OP}}$ c. $\stackrel{‾}{\mathrm{QR}}$ d. $\stackrel{‾}{\mathrm{TS}}$

#### Solution:

From the given figure, x-axis is the perpendicular bisector of both MT and NS. So, TS is the image of MN under a reflection in the x-axis.

10.
What is the image of $\stackrel{‾}{\mathrm{MN}}$ under a reflection in the $y$- axis?

 a. $\stackrel{‾}{\mathrm{MN}}$ b. $\stackrel{‾}{\mathrm{ST}}$ c. $\stackrel{‾}{\mathrm{PO}}$ d. $\stackrel{‾}{\mathrm{QR}}$

#### Solution:

From the given figure y-axis is the perpendicular bisector of both MP and NO. So, PO is the image of MN under the reflection in the y- axis.