Answer:
The coordinates of point B = (1, -4)
Step-by-step explanation:
Complete Question
Point A is at (−3,4) and point C is at (2,−6). Find the coordinates of point B on line AC such that the ratio of AB to AC is 4:5.
Solution
Point B divides line AC into two parts
A = (-3, 4)
C = (2, -6)
AB:AC = 4:5
If (AB/AC) = (4/5)
5AB = 4AC
But AC = AB + BC
5AB = 4(AB + BC)
5AB = 4AB + 4BC
5AB - 4AB = 4BC
AB = 4BC
(AB/BC) = (4/1)
AB:BC = 4:1
Hence, point B divides line AC internally into two parts with ratio 4:1
Mathematically, if a point P(x, y) divides the coordinates (x₁, y₁) and (x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + mx₁)/(m + n)]
y = [(my₂ + my₁)/(m + n)]
For this question,
x₂ = 2
x₁ = -3
y₂ = -6
y₁ = 4
m = 4
n = 1
Point B is then described with coordinates
x = [(4×2 + 1×-3)/(4+1)] = (5/5) = 1
y = [(4×-6 + 1×4)/(4+1)] = (-20/5) = -4
Hence, the coordinates of point B is given as
(x, y) = (1, -4)
Hope this Helps!!!
