Question

The endpoints of the directed line segment AB are A(−3, 4) and B(5, 10). Find the coordinates of point P along AB¯¯¯¯¯¯¯¯ so that the ratio of AP to PB is 1 to 3.

Answer 1

The coordinates of P is (-1,5.5)

Explanation:

Here, we want to find the coordinates of the point that divides the segment into the ratio 1 to 3

To do this, we are going to use the section formula

We have this as;

(x,y) = (nx1 + mx2)/m+ n, (ny1 + my2)/m + n

where m = 1 , n = 3

(x1,y1) = (-3,4)

(x2,y2) = (5,10)

Substituting these values, we have;

(x,y) = (3(-3) + 1(5)/4 , (3(4) + 1(10)/4

(x,y) = (-9+ 5)/4 , (12 + 10)/4

(x,y) = (-1, 5.5)