Mathematics
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.
Answer
Since, y = 3 is a straight line parallel to x-axis and at a distance of 3 units from it, therefore in the figure, AB represents y = 3.
Steps of construction :
- Mark P(4, 1) and Q(-2, 4) on the graph.
- From point P draw a straight line Perpendicular to AB and produce.
- On this line mark a point P' which is at same distance behind AB as P(4, 1) before it.
- From point Q draw a straight line Perpendicular to AB and produce.
- On this line mark a point Q' which is at same distance behind AB as Q(-2, 4) before it.
The graph is shown below:
From graph,
P' = (4, 5) and Q' = (-2, 2)
Hence, co-ordinates of P' = (4, 5) and Q' = (-2, 2).
Related Questions
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 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.
A point P (-2, 3) is reflected in the line x = 2 to point P'. Find the co-ordinates of P'.
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, when reflected in the y-axis. Write down the coordinates of P''. Find the coordinates of P''', when P is reflected in the line, parallel to y-axis such that x = 4.