The endpoints of AB are A (-4,8) and B (12,-4). How do you find the coordinates of P if P lies on AB and is 3/8 the distance from A to B?

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Answer 1 · 2018-07-28T02:46:59

#(\frac{4}{11}, \frac{52}{11})#

Assuming the point #P# lies on the line AB such that

#PA:PB=3:8\equiv m:n#

point #P# internally divides the line AB with end points #A(-4, 8)\equiv(x_1, y_1)# & #B(12, -4)\equiv(x_2, y_2)#.

The coordinates of point #P# are given by internal division formula as follows

#(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})#

#\equiv(\frac{3\cdot 12+8(-4)}{3+8}, \frac{3(-4)+8(8)}{3+8})#

#\equiv(\frac{4}{11}, \frac{52}{11})#