Question

6.) here are the pre - image and image coordinates of a figure. no grid has been provided. describe a possible transformation that took place for each set of pre - image and images.

pre - image coordinate	image coordinates	possible transformation
(-3, 5)	(-3, -5)
(6, -4)	(6, 4)

Explanation:

Step1: Analyze first pair

Pre - image: \((-2,1)\), Image: \((-2, - 1)\). The \(x\) - coordinate remains the same (\(-2=-2\)), the \(y\) - coordinate changes from \(1\) to \(-1\), which is a reflection over the \(x\) - axis (since for a reflection over the \(x\) - axis, the transformation is \((x,y)\to(x, - y)\)).

Step2: Analyze second pair

Pre - image: \((-3,5)\), Image: \((-3, - 5)\). The \(x\) - coordinate \(-3=-3\) (remains same), \(y\) - coordinate changes from \(5\) to \(-5\), which also follows the reflection over \(x\) - axis rule \((x,y)\to(x, - y)\).

Step3: Analyze third pair

Pre - image: \((6,-4)\), Image: \((6,4)\). The \(x\) - coordinate \(6 = 6\) (remains same), \(y\) - coordinate changes from \(-4\) to \(4\), which is again a reflection over the \(x\) - axis (\((x,y)\to(x, - y)\) as \(-(-4)=4\)).

Answer:

The possible transformation is a reflection over the \(x\) - axis. For each pre - image point \((x,y)\), the image point is \((x, - y)\).