Question

enlargement
reduction
what is the scale factor? *
1 point
1/4
1/2
2
3
4
if g= (-8,-8) what is the coordinate of g? *
1 point
(-4,-4)
(-2,-2)
(-1,-1)
(-8,-8)

Explanation:

Step1: Identify transformation type

The image G'H'I'J' is smaller than the original image GHIJ, so it is a reduction.

Step2: Find scale - factor

Let's consider the distance between corresponding points. For example, if we look at the x - coordinates of a point and its image. Suppose we consider a point and its image, and assume the original point has x - coordinate \(x_1\) and the image has x - coordinate \(x_2\). If we take a point and its image, and assume the original point \(G=(-8,-8)\) and its image \(G'\). The scale factor \(k\) is given by the ratio of the coordinates of the image to the original point. If we consider the x - coordinate of \(G\) and \(G'\), if \(x_{G}=-8\) and \(x_{G'}\) and assume the scale factor \(k\), then \(x_{G'}=k\times x_{G}\). By observing the graph, we can see that if we take \(G(-8, - 8)\) and \(G'\), the scale factor \(k=\frac{1}{2}\) since \(-4=\frac{1}{2}\times(-8)\) (for x - coordinate and same for y - coordinate).

Step3: Calculate coordinates of \(G'\)

Given \(G = (-8,-8)\) and scale factor \(k = \frac{1}{2}\), the coordinates of \(G'\) are \((\frac{1}{2}\times(-8),\frac{1}{2}\times(-8))=(-4,-4)\) using the formula \((x',y')=k(x,y)\) for a dilation with scale factor \(k\) centered at the origin.

Answer:

1. Reduction
2. 1/2
3. (-4, -4)