Question

Find the point, M, that divides segment AB into a ratio of 2:1 if A is at (-1, 2) and B is at (8, 15). A) (6, 8) B) (6, 26 3 ) C) (5, 32 3 ) D) (5, 26 3 )

Answer 1

C. 5, 32/3

Explanation:

(5,

32

3

) The sum of the ratio numbers (2+1) is 3, so M is

2

3

of the distance from A to B. The coordinates of M are (xm, ym), where xm = -1 +

2

3

(8 - (1)) and ym = 2 +

2

3

(15 - 2).

Answer 2

(5 , 10.67)

Explanation:

Given that a point M divides segment AB into a ratio of 2:1

A = (-1,2)

B = (8,15)

Formula to use:

x(M) = x1 + a / (a+b) (x2 - x1)

y(M) = y1 + a / (a+b) (y2 - y1)

where,

x1 = -1

x2 = 8

y1 = 2

y2 = 15

a : b = 2 : 1

a = 2

b = 1

Put values in the formula

x(M) = -1 + ( 2 / (2 + 1)) (8 + 1)

= 5

y(M) = 2 + 2 / (2 + 1) (15 - 2)

= 10.67