Question

calculating the scale factor of a reduction
the ordered pair (-4, 4) is on the pre - image. a scale factor was applied to produce the image on the coordinate plane.
what is the scale factor?
○ 1/4
○ 1/2
○ 2
○ 4

Explanation:

Step1: Identify image coordinates

From the graph, the image of \((-4, 4)\) (pre - image) should be found. Looking at the orange line, the corresponding image point seems to be \((-2, 2)\) (since the pre - image is at \((-4,4)\) and the image is halfway in terms of x and y coordinates).

Step2: Use scale factor formula

The scale factor \(k\) is given by the formula \(k=\frac{\text{image coordinate}}{\text{pre - image coordinate}}\). For the x - coordinate (or y - coordinate, since it's a reduction), pre - image x - coordinate \(x_{pre}=- 4\), image x - coordinate \(x_{image}=-2\). Then \(k = \frac{x_{image}}{x_{pre}}=\frac{-2}{-4}=\frac{1}{2}\). We can also check with the y - coordinate: pre - image y - coordinate \(y_{pre}=4\), image y - coordinate \(y_{image}=2\), \(k=\frac{y_{image}}{y_{pre}}=\frac{2}{4}=\frac{1}{2}\).

Answer:

B. \(1/2\)