Question

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 to the \(x\)-coordinate of each vertex

For a point \((x,y)\) and a scale factor \(k = \frac{4}{5}\), the new \(x\)-coordinate is \(x'=x\times k\).

• For \(P(5,15)\): \(x'_P = 5\times\frac{4}{5}=4\)
• For \(Q(15,15)\): \(x'_Q = 15\times\frac{4}{5}=12\)
• For \(R(15,10)\): \(x'_R = 15\times\frac{4}{5}=12\)
• For \(S(5,10)\): \(x'_S = 5\times\frac{4}{5}=4\)

Step2: Apply the scale factor to the \(y\)-coordinate of each vertex

The new \(y\)-coordinate is \(y'=y\times k\).

• For \(P(5,15)\): \(y'_P = 15\times\frac{4}{5}=12\)
• For \(Q(15,15)\): \(y'_Q = 15\times\frac{4}{5}=12\)
• For \(R(15,10)\): \(y'_R = 10\times\frac{4}{5}=8\)
• For \(S(5,10)\): \(y'_S = 10\times\frac{4}{5}=8\)

Answer:

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