Question

1. rectangle pqrs with vertices p(5,15), q(15,15), r(15,10), and s(5,10): k = 4/5 p (__, ) q (, ) r (, ) s (, __)

Explanation:

Step1: Apply the scale factor formula

When a point \((x,y)\) is dilated with a scale factor \(k\), the new point \((x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k = \frac{4}{5}\).
For point \(P(5,15)\):
\(x'_P=\frac{4}{5}\times5 = 4\)
\(y'_P=\frac{4}{5}\times15=12\)

Step2: For point \(Q(15,15)\)

\(x'_Q=\frac{4}{5}\times15 = 12\)
\(y'_Q=\frac{4}{5}\times15 = 12\)

Step3: For point \(R(15,10)\)

\(x'_R=\frac{4}{5}\times15=12\)
\(y'_R=\frac{4}{5}\times10 = 8\)

Step4: For point \(S(5,10)\)

\(x'_S=\frac{4}{5}\times5 = 4\)
\(y'_S=\frac{4}{5}\times10=8\)

Answer:

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