Respuesta :
Answer:
Stretching ΔDEF with the factor 5 will give D'(-10, 5), E'(-5,-5) and F'(-10,-10). Stretching ΔDEF with the factor 4 will give D'(-8, 4), E'(-4,-4) and F'(-8,-8).
Step-by-step explanation:
The Stretching is a distorting process of an object based on a scale factor. An object can be stretched either horizontally or vertically and sometimes both.
Stretch P'(x,y) = [tex]\left[\begin{array}{cc}h&0\\0&v\end{array}\right][/tex] × [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex].
where h is the horizontal factor and v is the vertical factor.
If the stretch factor is 5, for both horizontal and vertical direction.
D'(x,y)= [tex]\left[\begin{array}{cc}5&0\\0&5\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-2\\1\end{array}\right][/tex].
D'(x,y)=(-10,5).
E'(x,y)= [tex]\left[\begin{array}{cc}5&0\\0&5\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-1\\-1\end{array}\right][/tex].
E'(x,y)=(-5,-5).
F'(x,y)= [tex]\left[\begin{array}{cc}5&0\\0&5\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-2\\-2\end{array}\right][/tex].
F'(x,y)=(-10,-10).
Stretching ΔDEF with the factor 5 will give D'(-10, 5), E'(-5,-5) and F'(-10,-10).
If the stretch factor is 4, for both horizontal and vertical direction.
D'(x,y)= [tex]\left[\begin{array}{cc}4&0\\0&4\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-2\\1\end{array}\right][/tex].
D'(x,y)=(-10,4).
E'(x,y)= [tex]\left[\begin{array}{cc}4&0\\0&4\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-1\\-1\end{array}\right][/tex].
E'(x,y)=(-4,-4).
F'(x,y)= [tex]\left[\begin{array}{cc}4&0\\0&4\end{array}\right][/tex] × [tex]\left[\begin{array}{c}-2\\-2\end{array}\right][/tex].
F'(x,y)=(-8,-8).
Stretching ΔDEF with the factor 4 will give D'(-8, 4), E'(-4,-4) and F'(-8,-8).
