Line segment ab has endpoints a(7.5, 4.2) and b(2.3, 5.4). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1: 3.

  (6.2, 4.5)

Step-by-step explanation:

That point (P) will be the weighted average of the end points, where each weight is the proportion of the segment at the end farthest from the point:

  P = (3A +1B)/(3+1)

  = (3·7.5 +2.3, 3·4.2 +5.4)/4

  = (24.8, 18)/4

  = (6.2, 4.5)

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'.