Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated with a scale factor \(k\) centered at the origin \((0,0)\), the new coordinates \((x',y')\) are given by \((x',y')=(kx,ky)\). Here \(k = 5\).

Step2: Find the coordinates of point \(S\)

The original coordinates of \(S\) are \((-1,0)\). Using the dilation formula \((x',y')=(5\times(-1),5\times0)=(-5,0)\).

Step3: Find the coordinates of point \(T\)

The original coordinates of \(T\) are \((2,0)\). Using the dilation formula \((x',y')=(5\times2,5\times0)=(10,0)\).

Step4: Find the coordinates of point \(U\)

The original coordinates of \(U\) are \((2,-3)\). Using the dilation formula \((x',y')=(5\times2,5\times(-3))=(10,-15)\).

Step5: Find the coordinates of point \(V\)

The original coordinates of \(V\) are \((-1,-3)\). Using the dilation formula \((x',y')=(5\times(-1),5\times(-3))=(-5,-15)\).

Answer:

\(S'(-5,0)\), \(T'(10,0)\), \(U'(10,-15)\), \(V'(-5,-15)\)