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).

Answer 1

Answer:

(2, 4)

Step-by-step 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

Answer:

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

Step-by-step 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:

$(x,y) = (\frac{m1 x2 + m2 x1}{m1 + m2} ,\frac{m1 y2 + m2 y1}{m1 + m2})$

Using m1 : m2 = 3 : 1

Here, we get

$(x,y) = (\frac{3(4) +1(-4)}{1 +3} ,\frac{3(-10) + 1(-2)}{1 + 3})\\\implies (x,y) = (\frac{12-4}{4} ,\frac{-30-2}{4} )\\or, (x,y) = (\frac{8}{4} ,\frac{-32}{4} )$

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