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.

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Solution

Reflection in y-axis is given by M_y (x, y) = (-x, y)
A’ = Reflection of A(4, -1) in y-axis
A’ = (-4, -1)
Reflection in x-axis is given by M_x (x, y) = (x, -y)
B’ = Reflection of B in x-axis = (-2, 5)
Thus, B = (-2, -5)

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Q. Point

A (3, - 2)

on reflection in the x-axis is mapped as A' and point B on reflection in the y-axis is mapped onto

B^{'} (- 4, 3) .

(i) Write down the coordinates of A' and B.
(ii) Find the slope of the line A'B, hence find its inclination.

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.

(i) Plot the points A (3, 5) and B (-2, -4). Use 1 cm = 1 unit on both the axes.

(ii) A' is the image of A when reflected in the x-axis. Write down the co-ordinates of A' and plot it on the graph paper.

(iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B' and plot it on the graph paper.

(iv) Write down the geometrical name of the figure AA'BB'.

(v) Name two invariant points under reflection in the x-axis.

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

(a) Name the line of reflection.

(b) Write the co-ordinates of the image of (5, -8) in the line obtained in (a).

(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".

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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.

Reflection in y-axis is given by My (x, y) = (-x, y) A’ = Reflection of A(4, -1) in y-axis A’ = (-4, -1) Reflection in x-axis is given by Mx (x, y) = (x, -y) B’ = Reflection of B in x-axis = (-2, 5) Thus, B = (-2, -5)

Reflection in y-axis is given by M_y (x, y) = (-x, y)
A’ = Reflection of A(4, -1) in y-axis
A’ = (-4, -1)
Reflection in x-axis is given by M_x (x, y) = (x, -y)
B’ = Reflection of B in x-axis = (-2, 5)
Thus, B = (-2, -5)