Which rigid transformation(s) can map AMNP onto ATSR?
reflection only
rotation only
translation, then reflection
translation, then rotation

Option C

Step-by-step explanation:

Translation means moving the figure horizontally or vertically.

Reflection means flipping across a vertical or a horizontal line.

In the figure we see that we can vertically shift the point P to R down by some units.

Then we see that if we reflect that triangle NMP across the line which joins P & R we get the triangle STR.

So to have triangle MNP map onto to TSR we need to translate & then reflect.

Option C) is the right answer.

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

a c

step-by-step explanation: