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 \(S(-8,-6)\), \(T(-8,8)\), \(U(4,-8)\)

Step2: Apply the dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = \frac{1}{4}\)
For \(S(-8,-6)\):
\(x'=\frac{1}{4}\times(-8)=-2\), \(y'=\frac{1}{4}\times(-6)=-\frac{3}{2}\)
New coordinate \(S'(-2,-\frac{3}{2})\)
For \(T(-8,8)\):
\(x'=\frac{1}{4}\times(-8)=-2\), \(y'=\frac{1}{4}\times8 = 2\)
New coordinate \(T'(-2,2)\)
For \(U(4,-8)\):
\(x'=\frac{1}{4}\times4 = 1\), \(y'=\frac{1}{4}\times(-8)=-2\)
New coordinate \(U'(1,-2)\)

Step3: Plot the new points

Plot \(S'(-2,-\frac{3}{2})\), \(T'(-2,2)\), \(U'(1,-2)\) on the coordinate plane and connect them to form the dilated triangle.

Answer:

Plot the points \(S'(-2,-\frac{3}{2})\), \(T'(-2,2)\), \(U'(1,-2)\) and connect them.