Question

△bcd is dilated by a scale factor of \\(\frac{1}{3}\\) with the center of dilation at the origin. what are the coordinates of point d? ( ? , ? ) chart: a coordinate grid with triangle bcd, points b(6,3), c(6,6), d(9,3); and dilated points b(2,1), c(2,2)

Explanation:

Step1: Find coordinates of D

From the graph, point D has coordinates \((9, 3)\).

Step2: Apply dilation rule

When a point \((x, y)\) is dilated by a scale factor \(k\) with center at the origin, the new coordinates \((x', y')\) are given by \(x' = kx\) and \(y' = ky\). Here, \(k=\frac{1}{3}\), \(x = 9\), \(y = 3\).
So, \(x'=\frac{1}{3}\times9 = 3\) and \(y'=\frac{1}{3}\times3 = 1\).

Answer:

\((3, 1)\)