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The line segment joining A (3, 0) and B (5, 2) is rotated about A in the anticlockwise direction through an angle of 45° so that B goes to C. If D is the reflection of C in y-axis, find the coordinates of D.

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Here the slope of line AB =(2-0)/(5-3)=1

Then if θ, is the angle made by AB, with positive direction of x-axis,

We have tan θ = 1 => θ = 45 degree

Now if AB is rotated by 45 degree to AC,

The line segment AC makes 90 degree with x-axis.

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