Reflection in the Origin

Q. What is point symmetry?

Q.

The image of the pair of lines represented by ${\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0$ by the line mirror $\mathrm{y}=0$ is

1. ${\mathrm{ax}}^2–2\mathrm{hxy}–{\mathrm{by}}^2=0$

2. ${\mathrm{bx}}^2–2\mathrm{hxy}–{\mathrm{ay}}^2=0$

3. ${\mathrm{bx}}^2+2\mathrm{hxy}+\mathrm{ay}2=0$

4. ${\mathrm{ax}}^2–2\mathrm{hxy}+{\mathrm{by}}^2=0$

Q.

Use graph paper for this question.

Plot points A(-2, 4); B(2, 1) & C(-6, 1)

The line of symmetry of ∆ ABC & the line BC are both lines of symmetry of a quadrilateral ABCD.

a) Write the geometric name of the figure ABCD.

b) Write down the equations of the lines of symmetry of the quadrilateral ABCD.

1. Rectangle, y = 2, = -1

2. Rhombus, y = 1, = -2

3. Arrow head, y = 2, = 2

4. Rhombus, y = -1, = 2

5. Rectangle, y = 2, = -1

6. Parallelogram, y = 1, x = -2

7. Parallelogram, y =x, y = 1

Q.

The image of a point P(x, y) when reflected in the origin is ___

1. (0, -y)

2. (-x, y)

3. (x, -y)

4. (-x, -y)

Q.

On a graph paper, plot the triangle ABC, whose vertices are at the points A (3, 1), B(5, 0) and C (7, 4).

On the same diagram, draw the image of the triangle ABC under reflection in the origin O (0, 0).

Q.

A point P (3, 5) is reflected in the x - axis and then in the origin. The image P' will be

1. (-3, -5)

2. (3, -5)

3. (3, 5)

4. (-3, 5)

Q.

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C".

(i) Write down the co-ordinates of A", B" and C".

(ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".

Q.

Point A(4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.

Q.

A point $P$ is reflected in the $x=0$ and the coordinates of its image are$(-1,2).$

$i.$Find the coordinates of$P$

$ii.$Find the coordinates of the image $P$ under the reflection in the line$y=0$

$iii.$Find the coordinates of the image $P$under the reflection in the origin.

Q. Write the reflection of the following points with respect to origin.

1. ( 4 , 2 )
2. ( -2 , -3 )
3. ( -4 , 3 )
4. ( 4 , -9 )

Q.

State the co-ordinates of the followingpoints under reflection in origin :

(i) (-2, -4) (ii) (-2, 7) (iii) (0, 0)

Q.

Which one of the following has point symmetry about the origin?

1. 

2. 

3. 

4. 

Q.

Reflection of $(10,45)$ in the origin is ____________

1. (-10, -45)

2. (-10, 45)

3. (10, 45)

4. (10, -45)

Q.

Reflection of $(10,45)$ in the origin is ____________

1. (-10, 45)

2. (10, 45)

3. (10, -45)

4. (-10, -45)

Q. What are the points on the $y-$axis whose distance from the line $\frac{x}{3}-\frac{y}{4}=1$ is $2$ units.

Q.

The point P(5, 3) was reflected in the origin to get P'. If M is foot of the perpendicular from P to x -axis & N is foot of the perpendicular from P' to x -axis , Name the figure PMP'N

1. Paralleogram

2. Rectangle

3. Rhombus

4. Square

Q. Using graph paper, plot the points $A(6,4)$ and $B(0,4)$.
(i) Reflect $A$ and $B$ in the origin to get the images $A^{\prime }$ and $B^{\prime }$.
(ii) Write the co-ordinates of $A^{\prime }$ and $B^{\prime }$.
(iii) State the geometrical name for the figures $AB{A}^{\prime }{B}^{\prime }$.
(iv) Find its perimeter.

Q. Point A(4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.
$\left[2Marks\right]$

Q.

Point A (x, 5) is reflected in the origin and its image is (2, y). Write down the values of x and y.

1. None of these

2. $x=2,y=5$

3. $x=-2,y=-5$

4. $x=-2,y=5$

Q.

Reflection of the point $(1,-9)$ in the origin is $(-1,a)$. The value of $a$ is ___

Q.

Reflection of the point $(-2,9)$ in the origin is ___________

1. (-2, -9)

2. (-2, 9)

3. (2, -9)

4. (2, 9)

Q.

The image of the point (-7, -9) when reflected in the origin is___

1. (-7, 9)

2. (7, 9)

3. (7, -9)

4. (9, 7)

Q. Rectangle ABCD is reflected in the line y = -1.
What is the image of the point C?

1. $(4,-4)$
2. $(4,-7)$
3. $(4,0)$
4. $(-6,2)$

Q. Write the reflection of the following points with respect to origin.

1. ( 2 , 3 )
2. ( -4 , -2 )
3. ( 4 , -3 )
4. ( -4 , 9 )$\left[3Marks\right]$

Q.

The image of a point P (2, 3) under reflection in the origin is P'(x, y). Write down the values of x and y.

1. Can not be determined

2. None of these

3. $x=-2,y=-3$

4. $x=2,y=3$

Q.

The reflection of the point (x , y) in the origin is (-x, -y)

1. True

2. False

Q.

Find the coordinates of the image of each of the following points under the reflection in the origin.

$(\frac{1}{5},0)$

Q. The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ∆ABC.
(i) Write down the co-ordinates of $A_1,B_1,C_1$if $\Delta A_1{B}_1{C}_1$ is the image of ∆ ABC when reflected in the origin.
(ii) Write down the co-ordinates of $A_2,B_2,C_2$ if $\Delta A_2{B}_2{C}_2$ is the image of ∆ ABC when reflected in the x-axis.
(iii) Assign the special name to the quadrilateral $BC{C}_2{B}_2$ and find its area.

Q.

Verify Euler’s formula for the following graphs.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Q. What are the points on the $y-$axis whose distance from the line $\frac{x}{3}-\frac{y}{4}=1$ is $5$ units.