Question

Find the point, M, that divides segment AB into a ratio of 3:1 if A is at (-4, -2) and B is at (4, -10).

A) (8, 2)
B) (4, -2)
C) (-2, 4)
D) (2, -8)

Answer 1

(2, 4)

Explanation:

The sum of the ratio numbers (3+1) is 4, so M is [[3/4] of the distance from A to B. The coordinates of M are (xm, ym), where xm = =-4 + 3 /4 (4 - -(4)) and ym = -2 + 3 /4 (-10 - (-2)).

Answer 2

D) The coordinates of
`(x,y)  = (2, -8)`

Explanation:

The coordinates of the points are given as A(-4, -2) and B(4,-10).

The ratio is 3 : 1

Le t us assume the point is M (x,y).

⇒ AM : MB = 3 : 1

Now, Using SECTION FORMULA:

`(x,y)  = ((m1 x2 + m2 x1)/(m1 + m2) ,(m1 y2 + m2 y1)/(m1 + m2))`

Using m1 : m2 = 3 : 1

Here, we get

`(x,y)  = ((3(4)  +1(-4))/(1 +3) ,(3(-10) + 1(-2))/(1 + 3))\\\implies (x,y) = ((12-4)/(4) ,(-30-2)/(4) )\\or, (x,y) = ((8)/(4)  ,(-32)/(4) )`

Hence, the coordinates of
`(x,y)  = (2, -8 )`