What is the distance between (2, -1) and (-1,-5) on the coordinate plane?
7 units
6 units
5 units
4 units

5 units

Step-by-step explanation:

Let the two points be A and B

A(2,-1), B(-1,-5)

Where x1=2, x2=-1, y1=-1, y2= -5

Distance formula=√(x2-x1)^2+(y2-y1)^2

Distance formula=√(-1-2)^2+(-5+1)^2

=√(-3)^2+(-4)^2

=√9+16

=√25

=5 units

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'.