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: a(2,2), b(3,1), c(3,3), d? options for d: d(2,4), d(4,4), d(8,8), d(8,16). (with a coordinate grid showing figure abcd with points a(4,4), b(6,2), c(6,6), d(4,8))

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 \(D\) is \((4, 8)\).

Step2: Apply the dilation formula

For \(D(4, 8)\), multiply each coordinate by \(\frac{1}{2}\).
\(x\)-coordinate: \(4\times\frac{1}{2}=2\)
\(y\)-coordinate: \(8\times\frac{1}{2}=4\)
So the coordinates of \(D'\) are \((2, 4)\).

Answer:

\(D'(2, 4)\)