Mathematics
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 mirror line and write its equation.
(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.
Answer
(i) Given,
(-2, 0) ⇒ (2, 0) and (5, -6) ⇒ (-5, -6)
In both above transformation the sign of abscissa changes, which is possible after reflection in y-axis.
Hence, mirror line = y-axis, whose equation is x = 0.
(ii) Reflection in y-axis is given by,
My(x, y) = (-x, y)
∴ Image on reflection of (-8, -5) in mirror line (y-axis) = (8, -5)
Hence, co-ordinates of the image of (-8, -5) in the mirror line = (8, -5).
Related Questions
Attempt this question on graph paper.
(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
(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".
Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1; points (0, -3) and (0, 1) are invariant points on reflection in line L2.
(i) Name and write equations for the lines L1 and L2.
(ii) Write down the images of points P(3, 4) and Q(-5, -2) on reflection in L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the images as P" and Q" respectively.
(iv) State or describe a single transformation that maps P' onto P".
The points P(4, 1) and Q(-2, 4) are reflected in line y = 3. Find the co-ordinates of P', the image of P and Q', the image of Q.
A point P (-2, 3) is reflected in the line x = 2 to point P'. Find the co-ordinates of P'.