Determine the relationships between the following lines: * AB A (2, 5), B(6, – 11)
CĐ C (3, 10), D(-1, 9)

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  the lines are perpendicular

Step-by-step explanation:

You can tell something by looking at the differences of coordinates:

  B-A = (6-2, -11-5) = (4, -16) . . . . . Δy/Δx = -16/4 = -4

  D-C = (-1-3, 9-10) = (-4, -1) . . . . .  Δy/Δx = -1/-4 = 1/4

The product of the slopes of these lines is (-4)(1/4) = -1, so ...

  the lines are perpendicular

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'.

answer: 414,377,008

step-by-step explanation:

just multiply it