Question

Given segment AB with points (-4, 8) and (6, 3) respectively. Find the coordinates of point P that partitions Segment AB in the ratio 3:2. The answer should be entered in the form (x,y) with out any spaces between characters.

Answer 1

Answer:

$P = (2,5)$

Step-by-step explanation:

Given

$A(-4,8)$

$B(6,3)$

$m:n = 3 : 2$

Required

Determine P

Since P divides the segment into 3:2, P is calculated using

$P = (\frac{nx_1 +m x_2}{m+n},\frac{ny_1 + my_2}{m+n})$

Where

$(x_1,y_1) = (-4,8)$

$(x_2,y_2) = (6,3)$

$m:n = 3 : 2$

Substitute these values in the above formula:

$P = (\frac{2 * -4 +3 * 6}{3 + 2},\frac{2 * 8 + 3 * 3}{3 + 2})$

$P = (\frac{-8 +18}{3 + 2},\frac{16 + 9}{3 + 2})$

$P = (\frac{10}{5},\frac{25}{5})$

$P = (2,5)$