Areflection is a transformation that maps point p in a figure, over a line, ab^< > , such that for point c at the intersection.

 PC=P'C and tex]m\angle{ACP}=90^{\circ}[/tex]

Step-by-step explanation:

Given : A reflection is a transformation that maps point P in a figure over a line, AB, such that for point C at the intersection of AB and PP'.

We know that reflection creates a image equidistant from the line of reflection.

Thus,  PC=P'C

Also in reflection , a line drawn from the point is perpendicular to the line of reflection.

Therefore,

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4