Question

the figure below is dilated with the center of dilation at the origin and a scale factor of $\frac{1}{2}$ and then reflected over y - axis. what are the coordinates of the image of point q after these transformations?

Explanation:

1. First, identify the coordinates of point Q:

• From the graph, the coordinates of point Q are \((2,4)\).

1. Perform the dilation:

• The rule for dilation with the center of dilation at the origin \((0,0)\) and a scale - factor \(k\) is \((x,y)\to(kx,ky)\). Here, \(k = \frac{1}{2}\).
• For point Q\((2,4)\), after dilation, the new coordinates \(Q_1\) are \((\frac{1}{2}\times2,\frac{1}{2}\times4)=(1,2)\).

1. Perform the reflection over the y - axis:

• The rule for reflection over the y - axis is \((x,y)\to(-x,y)\).
• For point \(Q_1(1,2)\), after reflection over the y - axis, the new coordinates \(Q_2\) are \((-1,2)\).

Step1: Determine original coordinates

\(Q=(2,4)\)

Step2: Apply dilation

\(Q_1 = (\frac{1}{2}\times2,\frac{1}{2}\times4)=(1,2)\)

Step3: Apply reflection over y - axis

\(Q_2=(-1,2)\)

Answer:

\((-1,2)\)