# If point P(2,4) is translated parallel to the line y-x-1=0 through a distance of 3√2 units so that its ordinate is decreased and it reaches Q.If R is the mirror image of Q in the line y=x,its...

If point P(2,4) is translated parallel to the line y-x-1=0 through a distance of 3√2 units so that its ordinate is decreased and it reaches Q.If R is the mirror image of Q in the line y=x,its co-ordinates are:

A) (-1,1)

B) (-1,-1)

C) (1,1)

D) (1,-1)

Ans: D...how???

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### 1 Answer

P is the point (2,4). It is translated to Q `3sqrt(2)` units parallel to y-x-1=0 (ordinate decreases), then reflected over the line y=x to R. Find the coordinates of R:

The line y-x-1=0 has slope (gradient) of 1. Since `PQ=3sqrt(2)` then Q is at (-1,1).

** Draw a line with slope 1 through (2,4). Since the ordinate decreases Q is to the left and beneath P. PQ is the hypotenuse of a 45-45-90 right triangle whose legs are 3 units long. (The slope is 1; the slope of a line is equal to the tangent of the angle that is formed by the line and the x-axis -- this angle is 45 degrees since opposite over adjacent is 1 and `tan^(-1)(1)=45^@` .

Then Q is at (2-3,4-3) or (-1,1).**

Now reflect over the line y=x. This can be done by exchanging the x and y coordinates. Thus Q(-1,1) maps to R(1,-1)

**The answer is D: (1,-1)**

Reflect the lower left vertex of the triangle across the red line.