Question

3 fill in the blank 8 points
give the new coordinates for dilating rectangle pqrs with vertices p(5,15),
q(15,15), r(15,10), and s(5,10): ( k = \frac{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 are \((kx, ky)\).

Step2: Dilate point P(5,15)

For \(P(5,15)\) and \(k = \frac{4}{5}\), we calculate \(x\)-coordinate: \(5\times\frac{4}{5}=4\), \(y\)-coordinate: \(15\times\frac{4}{5}=12\). So \(P'(4,12)\).

Step3: Dilate point Q(15,15)

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

Step4: Dilate point R(15,10)

For \(R(15,10)\) and \(k = \frac{4}{5}\), \(x\)-coordinate: \(15\times\frac{4}{5}=12\), \(y\)-coordinate: \(10\times\frac{4}{5}=8\). So \(R'(12,8)\).

Step5: Dilate point S(5,10)

For \(S(5,10)\) and \(k = \frac{4}{5}\), \(x\)-coordinate: \(5\times\frac{4}{5}=4\), \(y\)-coordinate: \(10\times\frac{4}{5}=8\). So \(S'(4,8)\).

Answer:

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