Question

1. square mnop with vertices m(-7, -4), n(-4, -3), o(-3, -6), and p(-6, -7): k = 2 m (__, ) n (, ) o (, ) p (, __)

Explanation:

Step1: Recall the rule for dilation

When a point \((x,y)\) is dilated with a scale factor \(k\), the new point \((x',y')\) is given by \((x',y')=(kx,ky)\).

Step2: Calculate \(M'\)

For point \(M(-7,-4)\) and \(k = 2\), \(x'=2\times(-7)=-14\), \(y'=2\times(-4)=-8\). So \(M'(-14,-8)\).

Step3: Calculate \(N'\)

For point \(N(-4,-3)\) and \(k = 2\), \(x'=2\times(-4)=-8\), \(y'=2\times(-3)=-6\). So \(N'(-8,-6)\).

Step4: Calculate \(O'\)

For point \(O(-3,-6)\) and \(k = 2\), \(x'=2\times(-3)=-6\), \(y'=2\times(-6)=-12\). So \(O'(-6,-12)\).

Step5: Calculate \(P'\)

For point \(P(-6,-7)\) and \(k = 2\), \(x'=2\times(-6)=-12\), \(y'=2\times(-7)=-14\). So \(P'(-12,-14)\).

Answer:

\(M'(-14,-8)\), \(N'(-8,-6)\), \(O'(-6,-12)\), \(P'(-12,-14)\)