Well, a distance-preserving transformation is called a rigid motion, and the name suggests that it <em>moves the points of the plane around in a rigid fashion.</em>
A transformation is distance-preserving if the distance between the images of any two points and the distance between the two original points are equal.
If that's confusing, I get it; basically if you transform something, the points from the transformation are image points. Take the distance from a pair of image points, and take the distance from a pair of original points, and they should be the same for a <em>rigid </em>motion.
I keep emphasizing this b/c not all transformations preserve distance; a dilation can grow or shrink things. But if you didn't go over dilations, don't say nothin XD
I don’t know because you don’t show any chart
Answer:

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... ((x -2)/(x^2 +x -6))/((x^2 +5x +4)/(x +4))
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<em>Comment on simplifying rational expressions</em>
Division of fractions works the same whether you're working with numbers or polynomials (or anything else). Dividing by something is the same as multiplying by its inverse (reciprocal).
(a/b)/(c/d) = (a/b)·(d/c)
I learned this as "invert and multiply". I've recently seen it referred to as "copy dot flip", meaning you copy the numerator, use a dot symbol to indicate multipication, then flip the denominator (make its reciprocal) to become what you're multiplying by.
Slope: (y2-y1)/(x2-x1)
(-3+5)/(-1-7) = 2/-8 = -1/4
The answer is d) -1/4