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For the line segment ST, S has coordinates (6,2) and T is on the
y-axis. The midpoint,M, of ST is on the x-axis. Find the coordinates of T and M ?

  • math -

    Okay, this one you really really should plot out the coordinates. It will give you an approximate orientation of the line. If plotted it out and realized that ST is a diagonal segment with a POSITIVE slope (meaning it goes up from left to right, that let you know that the y value on the T coordinate MUST has a negative value). I was just trying to lead you through the basic steps on analyzing the problem, you'll find this is a very useful skill if you learn it.

    Yeah, this is a tough problem... I was able to solve it but I made an "assumption" which I'm not sure it is okay to make. Here's basically what I did. So I plotted my graph, then I drew a horizontal line from (6,2) to the y-axis to from a right angle with point T and the y axis. The horizontal line is 6 units long. Now here's my assumption, I drew a vertical line upward from the midpoint to the horizontal line and where they intersect, I say the length on each side is 3, assuming that they will divide into two equal parts... which I think should make sense, but I'm not 100% sure.

    This is really hard to explain without showing you the graph, so I hope you followed me with your graph looks like mine. Okay, I know that from the x-axis to point S, that's 2 units. So now you basically just formed a small right triangle with the lengths 2 and 3. You can see that the x value of midpoint is 3 units away from point S, thus midpoint should be (3,0).

    Find the length from midpoint to S then set that as the distance from midpoint to T to find out the y value on T (0,y).

    This is the best I can help. You should get some credits for trying even if it's wrong. Unless someone else here has a better idea than me...

  • math -

    Really not that hard

    let point T be (0,b), it is on the y-axis, and let the midpoint be M(a,0), it is on the x-axis.

    by the property of the midpoint:
    6+0)/2 = a
    so a=3

    and (b+2)/2 = 0
    so b=-2

    so T is (0,-2) and M is (3.0)

  • math -

    thanks alot for you

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