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in a reflection the image of the line y-2x=3 is the line 2y-x=9.find the axis of reflection.

The axis of reflection is the angle bisector of the two lines.

One of the properties of the axis of reflection is that any point lying on the line is equi-distant from both the original line and the image.

Distance of a point from a line Ax+By+C=0 is
±(Ax+By+C)/sqrt(A²+B²)

Can you take it from here?

YES

Y=x+4

First find the intersection point of these lines and then also take one point from the line y = 2x 3 and calculate the distance from the intersection point to this point on the line. So this distance is equal to the distance fron the intersection point to the point (x,y) on the line 2y - x = 9. Then after by equiting them you can find (x,y). And so find the mid point between these two points. Finaly by using this mid point and the intersection point of these lines We can get the axis of reflection.

• BASSO PGSS @ D/BRHAN grade 11 -

Y=0.988X+4.012 APPROXIMATLY Y=X+4

Y=5X/6 + 25/6