What is the distance between
-24 and 9
on a number line?

The distance between -24 and 9 is; 33.

While determining the distance between two points on the number line;

The absolute value of their difference is considered the distance between the two points.

In this case; the difference is;

However, the absolute value of -33 is; 33.

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the distance is 14 on the number line

the answer is 175.4379

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.