91Ó°ÊÓ

CRITICAL THINKING In Exercises 43–48, tell whether the polygons are always, sometimes, or never similar. two isosceles triangles

Find the coordinates of point P along the directed line segment \(\mathrm{AB}\) so that \(\mathrm{AP}\) to \(\mathrm{PB}\) is the given ratio. (Section 3.5) $$\mathrm{A}(1,-2), \mathrm{B}(8,12) ; 4 \text { to } 3$$

CRITICAL THINKING In Exercises 43–48, tell whether the polygons are always, sometimes, or never similar. a right triangle and an equilateral triangle

MAKING AN ARGUMENT Your sister claims that when the side lengths of two rectangles are proportional, the two rectangles must be similar. Is she correct? Explain your reasoning.

HOW DO YOU SEE IT? You shine a ?ashlight directly on an object to project its image onto a parallel screen. Will the object and the image be similar? Explain your reasoning.