Question

1. use coordinate notation to describe the dilation of triangle abc to triangle abc.

Explanation:

Step1: Find coordinates of vertices

Let's assume \(A(-6, 8)\), \(B(6, 4)\), \(C(6,-8)\), \(A'(- 3,4)\), \(B'(3,2)\), \(C'(3,-4)\)

Step2: Determine dilation rule

To get from the \(x\) - coordinate of a vertex of \(\triangle ABC\) to the \(x\) - coordinate of the corresponding vertex of \(\triangle A'B'C'\), we divide by 2. Similarly for the \(y\) - coordinates. The general rule for dilation about the origin \((0,0)\) in coordinate - notation is \((x,y)\to(kx,ky)\), where \(k\) is the scale factor. Here \(k = \frac{1}{2}\). So the coordinate - notation for the dilation is \((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)

Answer:

\((x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\)