Question 1: The triangle and is first reflected in the line onto triangle and then is reflected in the origin onto Write down the co-ordinates of :

(i) (ii)

Answer:

Question 2: A point P is reflected in the x-axis. Co-ordinates of its image are (8, -6).

(i) Find the co-ordinates of P.

(ii) Find the co-ordinates of the image of P under reflection in the y-axis.

Answer:

Answer:

‘Yes’, it is always true.

Question 4: Points (-5,0) and (4,0) are invariant points under reflection in the line ; points (0, – 6) and (0, 5) are invariant on reflection in the line

(a) Name or write equations for the lines and

(b) Write down the images of P(2, 6) and Q (-8, -3) on reflection in Name the images as and respectively.

(c) Write down the images of and on reflection in Name the images as and respectively.

(d) State or describe a single transformation that maps onto

Answer:

(a) We know that every point in a line is invariant under the reflection in the same line.

Since, points (-5, 0) and (4,0) lie on the x-axis, therefore Points (-5, 0) and (4, 0) are invariant under reflection in x-axis.

Given that the points (-5, 0) and (4,0) are invariant on reflection in line

Therefore The line is x-axis, whose equation is

Similarly, the given points (0, – 6) and (0, 5) lie on the y-axis and are invariant on reflection in line

Therefore The line L, is y-axis, whose equation is

(b) P’ = The image of P(2,6) in = The image of P(2,6) in x-axis = (2, -6)

Q’= The image of Q(-8, -3) in = The image of Q(-8, -3) in x-axis = (-8, 3)

(c) P” = The image of P(2,6) in = The image of P(2, 6) in y-axis = (-2, 6)

Q” = The image of Q(-8, -3) in = The image of Q(-8, -3) in y-axis = (8, -3)

(d) Since, Q’= (-8, 3) and Q” = (8, -3) and we know

Therefore the single transformation that maps Q’ onto Q” = Reflection in origin

Question 5: (i) Find the reflection of the point P(-1, 3) in the line x = 2.

(ii) Find the reflection of the point Q(2, 1) in the line y + 3 = 0.

Answer:

(i) P(5, 3) is the reflection of P(-1, 3) in the line x=2

(ii) Q'(2, -7) is the reflection of Q(2, 1) in the line y+3 = 0

Question 6: The points P(5, 1) and Q(-2, -2) are reflected in line x = 2. Use graph paper to find the images P’ and Q’ of points P and Q respectively in line x = 2. Take 2 cm equal to 2 units.

Answer:

The graph of line x =2 is the straight line AB, as shown below, which is parallel to y-axis and is at a distance of 2 units from it. Mark P(5, 1) and Q (-2, -2) on the same graph paper.

Mark P’ at the same distance behind AB as P is before it. Since P is 3 units before AB, its image. P’ will be 3 units behind AB. Clearly, the co-ordinates of P’ = (-1, 1).

In the same way, since Q(-2, -2) is 4 units before AB, its image Q’ will be 4 units behind AB. On marking position of Q’, we find : Q’ = (6, -2)

Question 7: Use a graph paper for this question. (Take two divisions = I unit on both the axes). Plot the points P (3,2) and Q (-3, -2). From P and Q, draw perpendiculars PM and QN on the x-axis.

(a) Write the co-ordinates of points M and N.

(b) Name the image of P on reflection in the origin.

(c) Assign the special name to geometrical figure PMQN and find its area.

(d) Write the co-ordinates of the point to which M is mapped on reflection in:

(i) x-axis, (ii) y-axis, (iii) origin. [ICSE Board 2003]

Answer:

(a) Co-ordinates of M = (3, 0) and Co-ordinates of N = (-3. 0)

(b) Image of P(3, 2) in origin = (-3, -2) = Q

(c) PMQN is a parallelogram

(d)

(i) M (3, 0) reflected in x-axis gives (3, 0)

(ii) M (3, 0) reflected in y-axis gives (-3, 0)

(iii) M (3, 0) reflected in origin gives (-3, 0)

Question 8: Using the graph paper for this question.

The points A(2, 3), B(4, 5) and C(7, 2) arc the vertices of

(i) Write down the coordinates of A’, B’, C’ if is the image of when reflected in the origin.

(ii) Write down the co-ordinates of A”, 8″, C” If is the image of when reflected in the x-axis.

(iii) Mention the special name of the quadrilateral BCC”B” and find its area. [ ICSE Board 2006]

Answer: