Question

give the new coordinates for dilating rectangle pqrs with vertices p(5, 15), q(15, 15), r(15, 10), and s(5, 10): k = 4/5
there is no picture for this question.
write the numerical answer (ie if you get 2 for your answer, type \2\ not \two\)
p( type your answer... , type your answer... )
q( type your answer... , type your answer... )
r( type your answer... , type your answer... )
s( type your answer... , type your answer... )

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) with a scale factor \(k\) centered at the origin, the new coordinates \((x',y')\) are given by \(x' = kx\) and \(y' = ky\).

Step2: Dilate point P(5, 15)

For \(P(5,15)\) and \(k=\frac{4}{5}\):
\(x'=\frac{4}{5}\times5 = 4\)
\(y'=\frac{4}{5}\times15 = 12\)
So \(P'(4,12)\)

Step3: Dilate point Q(15, 15)

For \(Q(15,15)\) and \(k = \frac{4}{5}\):
\(x'=\frac{4}{5}\times15=12\)
\(y'=\frac{4}{5}\times15 = 12\)
So \(Q'(12,12)\)

Step4: Dilate point R(15, 10)

For \(R(15,10)\) and \(k=\frac{4}{5}\):
\(x'=\frac{4}{5}\times15 = 12\)
\(y'=\frac{4}{5}\times10=8\)
So \(R'(12,8)\)

Step5: Dilate point S(5, 10)

For \(S(5,10)\) and \(k=\frac{4}{5}\):
\(x'=\frac{4}{5}\times5 = 4\)
\(y'=\frac{4}{5}\times10 = 8\)
So \(S'(4,8)\)

Answer:

\(P'(4,12)\)
\(Q'(12,12)\)
\(R'(12,8)\)
\(S'(4,8)\)