SOLUTION: Can you help me with this please? Find the coordinate, T , this is three-fifths of the distance from A(2,-2) to B(-3,8)

Question 960470: Can you help me with this please?
Find the coordinate, T , this is three-fifths of the distance from A(2,-2) to B(-3,8)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The distance from point A to point B is calculated with the following formula,
d = sqrt ( (x2-x1)^2 + (y2 - y1)^2 ) = sqrt ( (-3-2)^2 + (8-(-2))^2 ) = sqrt ( 25 + 100) = 5*sqrt(5)
******************************************
now 3/5 * 5*sqrt(5) = 3*sqrt(5) and
3*sqrt(5) = sqrt (x2 - 2)^2 + (y2 - (-2))^2)
square both sides of =
45 = (x-2)^2 + (y+2)^2
******************************************
now we want the equation of the line that connects points A and B
slope = 8+2 / -5 = -2
so far we have
y = -2x +b
use point A to find b
-2 = -2*2 +b
-2 = -4 +b
b = 2 and
y = -2x + 2
*****************************************
now substitute -2x+2 for y in the above equation (note that it is the equation of a circle with its center at point A)
45 = (x-2)^2 + (-2x+2+2)^2
45 = (x-2)^2 + (-2x+4)^2
45 = x^2-4x+4 + 4x^2-16x+16
45 = 5x^2-20x+20
divide both sides of = by 5
9 = x^2-4x+4
x^2 -4x -5 = 0
(x-5)*(x+1) = 0
we have two intersection points (substitute for x in our line equation)
(5,-8) and (-1,4)
***********************************
therefore T = (-1,4)

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