Question

Which diagram shows a reflection across y=−1/2x?

Answer 1

Option C) graph is correct

Explanation:

From the above , it is given that the line equation is y = (-1/2)(x)

This means that the line has negative slope.

From intuition one can say that, as preimage lies in first quadrant and line lying in second fourth quadrant, the image will lie in third quadrant.

Thus, the first option is eliminated.

the image of the point (x1,y1) in the line ax1+by1+c=0 is given by:

`(x-x1)/(a) =(y-y1)/(b) =(-2(ax1+by1+c))/(a^(2)+b^(2))`

Further if we take one point of preimage (2,3) and reflect it about y=(-1/2)(x) , we get the coordinate to be (-1,-4).

And so the this reflected point only lies in the third graph.

Thus third graph is the correct reflected graph.