Question

dilate figure abcd by a scale factor of \\(\frac{1}{2}\\) with the center of dilation at the origin. find the coordinates of the vertices of the dilated image. figure abcd: a(4,4), b(6,2), c(6,6), d(4,8); figure abcd options for a: a(2,2), a(2,4), a(4,2), a(8,8)

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) with center at the origin and scale factor \(k\), the new coordinates are \((kx,ky)\). Here, \(k = \frac{1}{2}\) and the point is \(A(4,4)\).

Step2: Apply the dilation formula

For point \(A(4,4)\), multiply each coordinate by \(\frac{1}{2}\). So, \(x\)-coordinate: \(4\times\frac{1}{2}=2\), \(y\)-coordinate: \(4\times\frac{1}{2}=2\). So the dilated point \(A'\) is \((2,2)\).

Answer:

\(A'(2,2)\)