Question

Find the coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1.

Answer 1

Answer:

$(x,y) = (\frac{27}{4}, -\frac{1}{2})$

Explanation:

Given

$(x_1,y_1) = (3,-2)$

$(x_2,y_2) = (8,0)$

$m : n = 3 :1$

Required

The coordinates of the point

This is calculated using:

$(x,y) = \frac{1}{m+n}(mx_2 + nx_1, my_2 + ny_1)$

So, we have:

$(x,y) = \frac{1}{3+1}(3*8 + 1*3, 3*0 - 1*2)$

$(x,y) = \frac{1}{4}(27, -2)$

So, we have:

$(x,y) = (\frac{27}{4}, -\frac{1}{2})$