Question

If A = (-4,6) and B = (6,-7), find:

(a) the coordinates of the point P on the line segment AB such that AP:Pb = 3:1

(b) the coordinates of the point P on the line AB such that AP:AB = 3:1 and P is closer to point B than to point A

Answer 1

The equation of AB is :
y = -13x/10 + 4/5
The equation of the perpendicular bisector of AB is: y = 10x/13 - 33/26
The distance between A and B is root(269)
The Midpoint AB is (1,-0.5)
Above Answers are all correct.
How to find the coordinates of P?

Answer 2

That means 3/4 of the way along the line segment from A to B

That means 3/4 in x and 3/4 in y

in x
-4 +(3/4)(6 - -4) = -4+ 3*10/4 =
= -16/4 +30/4 = 14/4 = 3 1/2

in y
6 + (3/4)(-7-6) = 6- 13*3/4
= 24/4-39/4 = -15/4 = -3 3/4
so
(3.5 , -3.75)

In part B same deal but times 3, not 3/4

Answer 3

Thanks a lot Damon

Answer 4

You are welcome