Answer:
C. (-1,-2)
Step-by-step explanation:
Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.
Let A = (xโ, yโ) = (5, 16), B = (xโ, yโ) and C = (x, y) = (3, 10)
So x = (mxโ + nxโ)/(m + n)
y = (myโ + nyโ)/(m + n)
Substituting the values of the coordinates, we have
x = (mxโ + nxโ)/(m + n)
3 = (1 ร xโ + 2 ร 5)/(2 + 1)
3 = (xโ + 10)/3
multiplying through by 3, we have
9 = xโ + 10
xโ = 9 - 10
xโ = -1
y = (myโ + nyโ)/(m + n)
10 = (1 ร yโ + 2 ร 16)/(2 + 1)
10 = (xโ + 32)/3
multiplying through by 3, we have
30 = yโ + 32
yโ = 30 - 32
yโ = -2
So, the coordinates of B are (-1, -2)
