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Question
Write down the co-ordinates of the image of the point (-2, 4) under reflection in the origin and under reflection in the y-axis. What is the distance between the points of reflection?
Solution
Let P be the point = (-2, 4 ).
Image under reflection in the origin P' = (2,-4)
Image under reflection in the y-axis p" = (2, 4)
Distance between points of reflection
= `sqrt ((4 - (-4))^2 + (2 - 2)^2)`
= `sqrt (8 ^2)`
= `sqrt 64`
= 8 units
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Use graph sheet for this question. Take 2 cm = 1 unit along the axes.
- Plot A(0, 3), B(2, 1) and C(4, –1).
- Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.
- Reflect point A in the line BB' and name its images as A'.
- Plot and write coordinates of point A'.
- Join the points ABA'B' and give the geometrical name of the closed figure so formed.
Study the graph and answer each of the following:
- Write the coordinates of points A, B, C and D.
- Given that, point C is the image of point A. Name and write the equation of the line of reflection.
- Write the coordinates of the image of the point D under reflection in y-axis.
- Whats the name given to a point whose image is the point itself?
- On joining the points A, B, C, D and A in order, a figure is formed. Name the closed figure.
