Question

graph the image of square qrst after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.

Explanation:

Step1: Find coordinates of original square

Assume \( Q(-9,-9) \), \( R(9,-9) \), \( S(9,9) \), \( T(-9,9) \).

Step2: Apply dilation formula

For a point \((x,y)\) with dilation centered at origin and scale factor \(k = \frac{1}{3}\), new coordinates \((x',y')=(k x,k y)\).

• For \( Q(-9,-9) \): \(x'=\frac{1}{3}\times(-9)= - 3\), \(y'=\frac{1}{3}\times(-9)= - 3\), new point \(Q'(-3,-3)\).
• For \( R(9,-9) \): \(x'=\frac{1}{3}\times9 = 3\), \(y'=\frac{1}{3}\times(-9)= - 3\), new point \(R'(3,-3)\).
• For \( S(9,9) \): \(x'=\frac{1}{3}\times9 = 3\), \(y'=\frac{1}{3}\times9 = 3\), new point \(S'(3,3)\).
• For \( T(-9,9) \): \(x'=\frac{1}{3}\times(-9)= - 3\), \(y'=\frac{1}{3}\times9 = 3\), new point \(T'(-3,3)\).

Step3: Plot new points

Plot \(Q'(-3,-3)\), \(R'(3,-3)\), \(S'(3,3)\), \(T'(-3,3)\) and connect them to form the dilated square.

Answer:

The image of square \(QRST\) after dilation has vertices \(Q'(-3,-3)\), \(R'(3,-3)\), \(S'(3,3)\), \(T'(-3,3)\). Plot these points and connect them.