Posted by neil on .
A point p(x,y) is on the line through A(4,4) and B(5,2).Find (a) the coordinates of P given that the segment AB is extended through B to P so that P is twice as far from A as far from B,and (b) the coordinates of P given that AB is extended through A to P so that P is three times as far from B as from A.

geometry 
Henry,
a. A(4,4), (B(5,2), P(x,y).
AP = 2BP,
x(4) = 2(x5),
x + 4 = 2x 10,
2x x = 4 + 10 = 14,
X = 14.
y 4 = 2(y2),
y 4 = 2y 4,
2y  y = 4 + 4 = 0,
Y = 0.
Solution set: P(14,0).
b. P(x,y), A(4,4), B(5,2).
PB = 3PA,
5  x = 3(4 x),
5  x = 12 3x,
x + 3x =  12  5,
2x =  17,
X = 17/2 = 8 1/2.
2  y = 3(4y),
2  y = 12  3y,
 y + 3y = 12  2,
2y =  10,
Y = 5
Solution set: P(8 1/2,5).