Mathematics
Given two points P and Q, and that (1) the image of P on reflection in y-axis is the point Q and (2) the mid point of PQ is invariant on reflection in x-axis. Locate (i) the x-axis (ii) the y-axis and (iii) the origin.
Answer
Given, Q is the image of P on reflection in y-axis and midpoint of PQ is invariant on reflection in x-axis.
From graph we get,
(i) x-axis will be the line joining the points P and Q.
(ii) The line perpendicular bisector of the line segment PQ is the y-axis.
(iii) The origin will be the mid point of the line segment PQ.
Related Questions
The triangle ABC where A(1, 2), B(4, 8), C(6, 8) is reflected in the x-axis to triangle A'B'C'. The triangle A'B'C' is then reflected in the origin to the triangle A''B''C''. Write down the coordinates of A'', B'', C''. Write down a single transformation that maps ABC onto A''B''C''.
The image of a point P on reflection in a line l is a point P'. Describe the location of the line l.
The point (-3, 0) on reflection in a line is mapped as (3, 0) and the point (2, -3) on reflection in the same line is mapped as (-2, -3).
(i) Name the mirror line.
(ii) Write the coordinates of the image of (-3, -4) in the mirror line.
Use graph paper for this question (take 2cm = 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).
(i) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD.
(ii) Write down the coordinates of A' and B'.
(iii) Name two points which are invariant under the above reflection.
(iv) Name the polygon A'B'CD.