Question

the figure below is dilated with the center of dilation at the origin and a scale factor of 1/2. what are the coordinates of the image of point t after this transformation?

Explanation:

1. First, assume the coordinates of point \(T\) are \((x,y)\).

• When a point \((x,y)\) is dilated with the center of dilation at the origin \((0,0)\) and a scale - factor \(k\), the coordinates of the image of the point \((x,y)\) after dilation are given by \((kx,ky)\).
• In this case, the scale - factor \(k = \frac{1}{2}\).

1. Then, find the new coordinates:

• Let's assume from the graph that the coordinates of point \(T\) are \((4, - 6)\) (since the point \(T\) is 4 units to the right of the \(y\) - axis and 6 units below the \(x\) - axis).
• Using the dilation formula \((kx,ky)\) with \(k=\frac{1}{2}\), \(x = 4\), and \(y=-6\), we have:
• The \(x\) - coordinate of the dilated point is \(k\times x=\frac{1}{2}\times4 = 2\).
• The \(y\) - coordinate of the dilated point is \(k\times y=\frac{1}{2}\times(-6)=-3\).

Answer:

The coordinates of the image of point \(T\) are \((2,-3)\).