Question

graph the image of (\triangle stu) after a dilation with a scale factor of (\frac{1}{4}), centered at the origin.

Explanation:

Step1: Find the coordinates of the original triangle

Assume the coordinates of \(S(-8,-4)\), \(T(-8,8)\), \(U(4,-8)\) (by observing the graph).

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(\frac{1}{4}x,\frac{1}{4}y)\).
For point \(S(-8,-4)\):
\(x'=\frac{1}{4}\times(-8)= - 2\), \(y'=\frac{1}{4}\times(-4)=-1\), so \(S'(-2,-1)\)
For point \(T(-8,8)\):
\(x'=\frac{1}{4}\times(-8)=-2\), \(y'=\frac{1}{4}\times8 = 2\), so \(T'(-2,2)\)
For point \(U(4,-8)\):
\(x'=\frac{1}{4}\times4 = 1\), \(y'=\frac{1}{4}\times(-8)=-2\), so \(U'(1,-2)\)

Step3: Plot the new points

Plot \(S'(-2,-1)\), \(T'(-2,2)\) and \(U'(1,-2)\) on the coordinate plane and connect them to form the dilated triangle \(\triangle S'T'U'\)

Answer:

Plot the points \(S'(-2,-1)\), \(T'(-2,2)\) and \(U'(1,-2)\) and connect them.