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The pint (4,1) undergoes the following three transformations successively (i) reflection about the line y = x. (ii) transformation through a distance 2 units along positive direction of x - axis (iii) rotation through an angle 45 degrees about the origin in the anticlockwise direction. What is the final position of the point after these transformations?
Answers (1)
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Let the point be (a, b) after the reflection.
now, since line joing (a,b) and (4,1 ) should be perpendicular to y =x
therefore,
b-1/a-4 = -1
=> b -1 = 4 - a ------------------(1)
also mid point of (a,b) and (4, 1) should lie on y =x.
=> b+1 = 4 +a -------(2)
from (1) and (2)
2b = 8
=> b =4
and a = 1
teherfore point after reflection is (1,4)
now teher is increment of 2 units along x axis
=> point is now (3,4)
Now let (x', y') be the point after rotation.
x' = 3 cos45 + 4 sin 45 = 7/(2)1/2
y ' = -3 sin 45 + 4 cos45= 1/(2)1/2