Question

Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

divides AB two-thirds from A to B?

Answer 1

`((21)/(5) ,(28)/(5) )` is the point

Explanation:

A(3, 2) and B(6, 11)

The ratio that divided AB is 2:3

we use section formula

2:3 is m:n

formula is
`((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n) )`

A(3, 2) is (x1,y1) and B(6, 11) is (x2,y2)

Plug in the value in the formula

`((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n) )`

`(((2)(6)+3(3))/(2+3) ,(2(11)+3(2))/(2+3) )`

`((21)/(5) ,(28)/(5) )`

Answer 2

The formula for a directed line is:

X = K1(X2) + (K2(X1) / K3

Y = K1(Y2) + (K2(Y1) / K3

K1 = numerator = 2

K2 = denominator - numerator = 3-2 = 1

K3 = denominator = 3

X = (2(6) + 1(3)) /3

X = (12+3) / 3

X = 12/3

X = 5

Y = (2(11) + 1(2)) /3

Y = (22 + 2) /3

Y = 24/3

Y = 8

The point is (5,8)