What are coordinates of the point on the directed line segment from (-2,6) to (3,-9) that partitions the segment into a ratio of 3 to 2? Can u please explain step by steps if possible

Answer 1

The explanation depends on the so-called Side-splitter Theorem from plane geometry.

If you draw a line segment and make it the hypotenuse of a right triangle, then draw lines parallel to the legs of the right triangle, the Side-splitter Theorem will show you how to get the answer below.

If the co-ordinates of the ends of the line segment are A(a,b) and C(c,d) and you want a point 100p% of the way from A to C, the co-ordinates are

abscissa: p*c+(1-p)a

ordinate: p*d+(1-p)b

In your case p=.6 (3/5) and 1-p=.4(2/5).

You got the whole lesson.

I hope it helps.