Point a is located at (4, 8) and point b is located at (14, 10) . what point partitions the directed line segment ab¯¯¯¯¯ into a 1: 3 ratio

point is (13/4 , 17/2)

Step-by-step explanation:

Let (x1,y1) and (x2,y2) be the end points of a line segment, 'A' is the point on the line segment such that A divides the line segment in the ratio p : q then the coordinates of A (x,y) is given by,

x = x1 + p/w(x2 - x1)  and y= y1 + p/w(y2 - y1) where w = p+q

It is given that,

Point A is located at (4, 8) and point B is located at (14, 10) .

Let P be the point on AB such that P divides AB in the ratio 1:3

Find the coordinates of P(x,y)

w = 1+3 = 4

x = x1 + p/w(x2 - x1) = 4 + 1/4(14 -4) = 4 + 10/4 =13/4

y= y1 + p/w(y2 - y1)  = 8 + 1/4(10 - 8) = 8 + 1/2 = 17/2

point is (13/4 , 17/2)