Mathematics
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).
Answer
(a) Reflection in y-axis is given by,
My(x, y) = (-x, y)
The transformation (-5, 0) ⇒ (5, 0) is similar to above transformation.
∴ It is reflection in y-axis.
Hence, y-axis is the line of reflection.
(b) Reflection in y-axis is given by,
My(x, y) = (-x, y)
∴ Image of (5, -8) in y-axis = (-5, -8).
Hence, image of (5, -8) in line of reflection = (-5, -8).
Related Questions
Points (-5, 1) and (4, 1) are invariant points under reflection in the line L.
Statement 1: The equation of the line L is x = 1.
Statement 2: A point P is called an invariant point with respect to a given line L, if its image in the line L is the point P itself.
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
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.
The point P(3, 4) is reflected to P' in the x-axis and O' is the image of O(origin) in the line PP'. Find :
(i) the coordinates of P' and O'.
(ii) the length of segments PP' and OO'.
(iii) the perimeter of the quadrilateral POP'O'.
(iv) the geometrical name of the figure POP'O'.
A(1, 1), B(5, 1), C(4, 2) and D(2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?