what are the coordinates of point c on the direct segment from A(-4,-10) to B(1,4) that partitions the segment such that AC:CB is 2:3

Question

what are the coordinates of point c on the direct segment from A(-4,-10) to B(1,4) that partitions the segment such that AC:CB is 2:3 please give the formula and help

Answer 1

formula is

(x1 * n + x2 * m)/(m+n)

(y1 * n + y2 * m)/(m+n)

(x1,y1) = (-4,-10) and (x2,y2)=(1,4) with m+n = 2+3=5

C is at:

(-4 * 3 + 1*2)/5 , (-10*3 + 4*2)/5

(-12+2)/5, (-30+8)/5

(-10/5 , -22/ 5) =

(-2, -22/5)

check

AB = sqrt ( 25 + 196) = sqrt( 221)

AC : (-4,-10) vs (-2, -22/5)

sqrt ( 4 + (-10 - (-22/5))^2 )

= sqrt ( 4 + [( -50 + 22)/5]^2 )

= sqrt( 4 + [ (-28/5]^2 )

= sqrt( 4 + 784/25 )

= sqrt [( 100 + 784)/25]

= sqrt( 884)/ 5

= sqrt( 4*221)/5 =

(2/5) sqrt(221)