Image of a Point with Respect to X = a

Q.

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

i) Plot the points A (–2, 0), B (4, 0) and C (1, 4) on the graph.

ii) Plot D (–2, 4) and E (4, 4). Assign special name to quadrilateral ABED.

iii) Draw lines of symmetry of quadrilateral ABED, and DABC.

iv) Write the equation of lines of symmetry.

1. y = 2, x = 1

2. y = -1, x = 2

3. y = 2, x = -1

4. y = -2, x = 4

Q.

Use graph paper for this question.

A(0, 3), B(3, -2) & O(0, 0) are the vertices ∆ ABO.

Plot the ∆ on a graph taking 2 cm = 1 unit on both axes.

Plot point D, which is the reflection of B in the Y axis.

a) Give geometrical name to the figure ABOD.

b) Write the equation of line of symmetry of figure ABOD.

1. Rectangle, = 0

2. Arrow head, = 0

3. Rhombus, x = 0

4. Square, y = 0

5. Arrow head, = 0

6. Rhombus, x = y

7. Pentagon, x = 2y

8. Pentagon, x = 0

Q.

What is the reflection of the point $A(1,2)$ in the line $x=1$?

1. (1, -2)

2. (-1, -2)

3. (-1, 2)

4. (1, 2)

Q.

A point P(-2, 3) is reflected in the line x = 2 to point P'. Find the coordinates of P'.

1. (8, 3)

2. (4, 3)

3. (6, 3)

4. (2, 3)

Q.

Complete the following table :

Point Transformation Image

(a) (5, -7)-------------------------------(-5, 7)

(b) (4, 2) Reflection x-axis ---------

(c) --------- Reflection in y-axis (0, 6)

(d) (6, -6) ----------------- (-6, 6)

(e) (4, -8) ------------------ (-4, -8)

Q.

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image :

(a) A' of A under reflection in the x-axis.

(b) B' of B under reflection in the line AA".

(c) A" of A under reflection in the y-axis.

(d) B" of B under reflection in the line AA".

Q.

Use graph paper for the question. Plot points A(4, 6) & B(1, 2).

A’ is the image of A when reflected in – axis.

B’ is the image of B when B is reflected in AA’.

Write the geometric name of the figure ABA’B’.

1. Square

2. Rectangle

3. Parallelogram

4. Kite

5. Rhombus

Q.

Find the image of point (4, -6) under the following operations :

(i) $M_x.M_y$ (ii) $M_y.M_x$

(iii) $M_o.M_x$ (iv) $M_x.M_o$

(v) $M_o.M_y$ (vi) $M_y.M_o$

Write down a single transformation equivalent to each operation given above.

State whether :

(a) $M_o.M_x$ = $M_x.M_o$

(b) $M_y.M_o$ = $M_o.M_y$

Q.

A triangle has coordinates (1, 4), (3, 4), and (3, 2), the image of the triangle when reflected in the line x = 4 will have coordinates -

1. (7 , 4), (5, 4) and (5, 2)

2. (-7 , -4), (5, 4) and (5, 2)

3. (7 , 4), (-5, -4) and (5, 2)

4. (7 , 4), (-5, -4) and (-5, -2)

Q.

P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P' and Q in the y-axis to Q'. State the co-ordinates of P' and Q'.

Q.

A point P is reflected in the x-axis, co-ordinates of its image are (-4, 5).

(i) Find the co-ordinates of P.

(ii) Find the co-ordinates of the image of P under reflection in the y-axis
$\left[3Marks\right]$

Q. The point which divides the line segment joining the points A(7, −6) and B(3, 4) in the ratio 1 : 2 lies in

(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant

Q. Use graph paper for this question (Take $2$cm $=$ $1$unit along both x and y axis). ABCD is a quadrilateral whose vertices are $A(2,2),B(2,-2),C(0,-1)$ and $D(0,1)$. Name two points which are invariant under the above reflections.

Q.

Find the co-ordinates of the following points when reflected in the line line x = 2.

i) (4, 1)

ii) (3, -2)

iii) (6, -2)

1. (0, 1), (1, -2) and , (-2, -2)

2. (0, 1), (1, -2) and , (2, 2)

3. (0, 1), (1, 2) and , (-2, -2)

4. (0, -1), (1, -2) and , (-2, -2)

Q. The image of the point $A(1,2)$ by the line mirror $y=x$ is the point $B$ and the image of $B$ by the line mirror $y=0$ is the point $(\alpha ,\beta )$, then:

1. $\alpha =1,\beta =-2$
2. $\alpha =0,\beta =0$
3. $\alpha =2,\beta =-1$
4. none of these

Q. A point P ( -2, 3 ) is reflected in line $x=2$ to point P'. Then the co-ordinates of P' is (2, 3).

1. False
2. True

Q.

State the co-ordinates of the following points under reflection in y-axis :

(i) (6, -3) (ii) (-1, 0) (iii) (-8, -2)

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 $(-5,-6).$
State the co-ordinates of the image of $(-8,-5)$ in the mirror line.

Q. A ray of light is sent along the line which passes through the point $A(2,3)$. The ray is reflected from the point $P$ on $x$ axis. lf the reflected ray passes through the point $(6,4)$, then the cordinates of point $P$ are

1. $\left(\frac{26}{7},0\right)$
2. $(0,0)$
3. $(0,\frac{26}{7})$
4. $(-\frac{26}{7},0)$

Q. The Trapezoid ABCD, shown in the above figure, is reflected over the y-axis to $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$, find the co-ordinates of $D^{\prime }$.

1. $(-12,1)$
2. $(-12,-1)$
3. $(12,-1)$
4. $(1,-12)$

Q.

The coordinate of a point and its image after a reflection are given. Identify the line of reflection.

$(2,1)\to (2,-1)$

Q.

A point P(3, 4) is reflected in line x + 3 = 0. Then the image of P is

1. (-5, 4)

2. (-8, 4)

3. (-9, 4)

4. (-6, 4)

Q.

A point P(-4, 5) is reflected in line y = 3 to P'. Find the coordinates of P'.

1. (-5, 2)

2. (-5, 1)

3. (-4, 2)

4. (-4, 1)

Q. The reflection of the complex number $\frac{4+3i}{1+2i}$ in the straight line $iz=\overline{z},$ is

1. $2+i$
2. $1+2i$
3. $2-i$
4. $1-2i$

Q. In figure, if triangle $ABC$ is reflected over line l, find the reflected coordinates of point B.

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

Q. Plot the points A (2, -3), B (-1, 2) and C (0, -2) on the graph paper. Draw the triangle formed by reflecting these points in the x-axis. Are the two triangles congruent?