analytic geometry. pls help?

I'm going to start by graphing (7,3) on the Cartesian plane. Now, I make an assumption that x < 7. (I plotted a point at approximately (2,6) just to see how the segment will run.)

It looks like, based on the assumptions I've made, y has to be less than 3. (I extended my line from the hypothetical location of (x,6), through (7,3), and plotted the hypothetical location of (9,y) on the line.

Now, I'm considering two things: the differences in the ordinates between (x,6) and (7,3) is 6-3, or 3.

The differences in the abscissas between (7,3) and (9,y) is 2.

Since (7,3) is the midpoint or our segment, on our graph we need to go left 2 and up 3 from (7,3) and right 2 and down 3 from (7,3).

This gives us endpoints of (5,6) and (9,0).

As you recall, we made an initial assumption that x > 7.

x could be greater than 7. I'd suggest you work the process through again, initially plotting (x,6) at approximately (10,6) but label it (x,6). However, if we draw the segment from (7,3) to (x,6), then (7,3) will not bisect the line between (x,6) and (9,y). Therefore, there is only one solution, which is found above. It's good to consider all the possibilities, though, especially when we've made some assumptions in the beginning.

I hope this helped.

because the point (7,3) bisectes the line segment ,so 2*7=x+9 and 2*3=6+y;

so here we go,the x=5and y=0;

(x,6) and (9,y)

7 = (x + 9) / 2

14 = x + 9

x = 5

3 = (6 + y)/2

6 = 6+y

y = 0

x+9/2=7,x=5

6+y/2=3 , y=0

(5,6) and (9,0) are the two points.