What is the distance between the points (-4, 2) and (1, -3) on the coordinate plane?
a. 7.07 units
b. 2.83 units
c. 5.83 units
d. 7.21 units

A. 7.07 units

Step-by-step explanation:

Use the distance formula for coordinates:

Fill in the coordinates accordingly:

which simplifies down to

which is of course

Plug that into your calculator and you'll get the answer

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'.