Mathematics
The point P(5, 3) was reflected in the origin to get the image P'.
(a) Write down the co-ordinates of P'.
(b) If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.
(c) If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.
(d) Name the figure PMP'N.
(e) Find the area of the figure PMP'N.
Reflection
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Answer
The graph is shown below:
(a) From graph,
Co-ordinates of P' = (-5, -3).
(b) From graph,
Co-ordinates of M = (5, 0).
(c) From graph,
Co-ordinates of N = (-5, 0).
(d) From graph,
Figure PMP'N is a parallelogram.
(e) As diagonal divides parallelogram into two triangles of equal area.
From graph,
Diagonal NM divides parallelogram into two right angle triangle of equal area.
∴ area of △NMP = area of △NMP'
Since, 1 block = 1 unit
So, NM = 10 and NP = 3
area of △NMP = x NM x NP = x 10 x 3 = 15 sq. units.
∴ area of △NMP' = 15 sq. units
From graph,
area of || gm PMP'N = area of △NMP + area of △NMP' = 15 sq. units + 15 sq. units = 30 sq. units.
Hence, area of || gm PMP'N = 30 sq. units.
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Related Questions
Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image :
(a) A' of A under reflection in the x-axis.
(b) B' of B under reflection in the line AA'
(c) A" of A under reflection in the y-axis.
(d) B" of B under reflection in the line AA''.
(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.
Point (5, 6) is reflected in a line to get the point (-5, 6). The line of reflection is :
x-axis
x = 5
y = 0
y-axis
(i) Point A is reflected in y-axis to get point B.
(ii) Point B is reflected in origin to get point C.
(iii) Point C is reflected in y = 0 to get point P. Now, which of the following coincides with point P.
Point A
Point B
Points B and C
Points A and B