Reflection

Q. Write the coordinates the reflections of points (3, 5) in X and Y -axes.

Q.

The image of the point (1, 5) when reflected in a line
LM is (9, 5). Write down the equation of the line
LM.

(ICSE)

Q.

Find the coordinates of the image of the point $(5,-3)$ under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.

1. $\left(i\right)(5,3)\left(ii\right)(-5,3),\left(iii\right)(-5,-3)$

2. $\left(i\right)(5,3)\left(ii\right)(-5,-3),\left(iii\right)(-5,3)$

3. $\left(i\right)(-5,-3)\left(ii\right)(5,3),\left(iii\right)(-5,3)$

4. $\left(i\right)(-5,3)\left(ii\right)(-5,-3),\left(iii\right)(5,3)$

Q.

The reflection of A (2, 3) in the line y = x is A' (3, 2). Write down the co-ordinates of the image of each of the points reflected in the line y = x
(i) (4, 1)
(ii) (- 2, - 3).

1. (i) (1, 4)
   (ii) (-3, -2)

2. (i) (1, -4)
   (ii) (-2 , 3)

3. (i) (1, 4)
   (ii) (-3, -2)

4. Coordinates will remain unchanged for both (i) and (ii).

Q.

(a) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q.

(b) The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.

(c) Name the figure PQR.

(d) Find the area of figure PQR.

Q.

Show that (a, 1), (b, 1) and (c, 1) are collinear points

Q.

Use graph paper for this question.

Plot points A(4, 4); B(4, –6) & C(8, 0).

Reflect ABC on the y – axis and name it A’, B’& C’

a) Write the geometric name of the figure AA’C’B’BC.

b) Identify the line of symmetry of the figure AA’C’B’BC.

1. Hexagon, = 0

2. Arrow head, = 2y

3. Hexagon, y = 0

4. Rectangle, x = y

5. Rhombus, = 0

6. Rectangle, = 0

7. Rhombus, x = y

8. Arrow head, y = 0

Q.

A $△$ ABC where A (1, 2), B (4, 8) and C (6, 8) is reflected in the origin to $△$ $A_1{B}_1{C}_1$. $△$ $A_1{B}_1{C}_1$ is then reflected in the x - axis to $△$ A₂, B₂, C₂. Write down the coordinates of A₂, B₂, C₂. Which single transformation could have provided the final co-ordinate of A₂, B₂, C₂?

1. $A_2(-1,2),B_2(-4,8),C_2(-6,8)$,
   Transformation through y-axis

2. $A_2(-1,2),B_2(-4,8),C_2(-6,8)$,
   Transformation through x-axis

3. None of these

4. $A_2(1,2),B_2(4,8),C_2(-6,8)$,
   Transformation through origin

Q.

(i) Point P (a, b) is reflected in the x-axis to P' (5, -2). Write down the values of a and b.

(ii) P" is the image of P when reflected in the y-axis. Write down the co-ordinates of P".

(iii) Name a single transformation that maps P' to P".

Q.

Plot the points A(4, 6) and B (1, 2). If A' is the image of A when reflected in the X axis and B' is the image of B when reflected in the line AA'. then the figure ABA'B' so formed is a

1. Kite

2. Rhombus

3. Parallelogram

4. Square

Q.

Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper.

(b) Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper.

(c) Write down :

(i) the geometrical name of the figure ABB' A';

(ii) the measure of angle ABB';

(iii) the image A" of A, when A is reflected in the origin.

(iv) the single transformation that maps A' to A".

Q.

The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

Q.

An isosceles right angled triangle is reflected about its hypotenuse. The figure formed by the triangle and its reflection is

1. Rectangle

2. Parallelogram

3. Rhombus

4. Square

Q. What will be an angle of reflection if a ray of light strikes the mirror normally?

1. ${180}^{\circ }$
2. ${90}^{\circ }$
3. $0^{\circ }$
4. ${360}^{\circ }$

Q.

A point P(2, -4) is reflected in the line x = 0 to get image Q. Point Q is reflected in the line y = 0 to get the image R. Find the area of figure PQR.

1. 12 sq units.

2. 18 sq units.

3. 24 sq units.

4. 16 sq units.

Q.

A point P (a, b) is reflected in the x-axis to P' (2, 3). Write down the values of a and b. P" is the image of P, reflected in the y-axis. Write down the co-ordinates of P". Find the co-ordinates of P", when P is reflected in the line, parallel to y-axis, such that x = 4.

Q. 1. If (a, b) is the midpoint of the line segment joining the points A(10, -6)& B(k, 4) and a-2b=18, then find the value of k and the distance AB.

Q.

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

Q.

Use graph paper and taking $1cm=1unit$ along with $x-axis$ and $y-axis$
Plot the point $A(-4,4)$ and $B(2,2)$
Reflect $A$ and$B$ in the origin to get the image $A$ and $B$respectively.
Write the coordinates of $A$and$B$
Give the geometric name for the figure $ABAB$

Q.

Points A & B have coordinates (7, 3) & (1, –9) respectively. Find

1. 2; 2y + + 2 = 0; p = 0

2. 2; 2y + - 2 = 0; p = 0

3. 2; 2y – – 2 = 0; p = 1

4. -2; 2y + – 2 = 0; p = 1

5. 1; 2y – – 2 = 0; p = 0

Q.

The slope of the line that is parallel to x – axis is __.

Q. Assertion (A)
The point P(−1, 6) divides the join of A(−3, 10) and B(6, −8) in the ratio 2 : 7.

Reason (R)
If the point C(x, y) divides the join of A(x₁, y₁) and B(x₂, y₂) in the ratio m : n, then $x=\frac{m{x}_2+n{x}_1}{m+n}\mathrm{and}y=\frac{m{y}_2+n{y}_1}{m+n}.$

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q.

ABCD is a parallelogram where A (3, –3); B (5, 8); C (4, 7) & D(, y).

Find the coordinates of D & equation of diagonal BD.

1. D(2 , 4); y = 4 + 12

2. D(2 , –4); y = 4 – 12

3. D(2 , –3); y = 4 + 6

4. D(2 , 4); y = 4 + 8

5. D(2 , 6); y = 4 + 12

Q. Based on the points and their images given below, match the following with respect to their transformation.

1. Reflection in origin
2. Reflection in y-axis
3. Reflection in x-axis
4. Invariant point

Q.

Find the coordinates of the image of the point $(5,-3)$ under (i) reflection in the x- axis (ii) reflection in the y- axis and (iii) reflection in the origin.

1. $\left(i\right)(-5,3)\left(ii\right)(-5,-3),\left(iii\right)(5,3)$

2. $\left(i\right)(5,3)\left(ii\right)(-5,-3),\left(iii\right)(-5,3)$

3. $\left(i\right)(5,3)\left(ii\right)(-5,3),\left(iii\right)(-5,-3)$

4. $\left(i\right)(-5,-3)\left(ii\right)(5,3),\left(iii\right)(-5,3)$

Q.

The image of point (3, 2) under the operation $M_o.M_y$ is

1. (-3, 2)

2. (3, 2)

3. (-3, -2)

4. (3, -2)

Q.

In the given figure P is the object and P' is the image. The line AB is which is the perpendicular bisector of PP' is called as ______.

1. mirror line

2. mediator

3. plane line

4. None of the above

Q.

The above figure is a square. Find the value of $x_1+y_1+x_2+y_2+x_3+y_3$ .

Q.

The point P(3, 4) is reflected to P' in the x axis and O' is the image of O(0, 0) when reflected in the line PP'. Find the perimeter of the quadrilateral POP'O'.

1. 22 units

2. 25 units

3. 16 units

4. 20 units

Q.

A(2, 6), B(6, 6) and C(6, 3) are the coordinates of a triangle. D, E and F are the reflection points of A, B and C respectively about X = 0. G, H and K are the reflection points of D, E and F respectively about Y = 1. The value of (sum of the y - coordinates of H and K) - (sum of the x - coordinates of G and H) is

1. 2

2. 3

3. 0

4. 1