Point A is located at (4, 8) and point B is located at (14, 10).What point partitions the directed line segment AB into a 1:3 ratio?a) (6 1/2, 8 1/2)b) (9, 9)c) (6, 6)d) (11 1/2, 9 1/2)
Accepted Solution
A:
Visualize the problem. We will have to use the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Let the unknown point be (x,y). The solution is as follows:
Distance between A and the point. 3 = √(4 - x₁)² + (8 - y₁)² 9 = 16 - 8x₁ + x₁² + 64 - 16y₁ + y₁² --> eqn 1
Distance between point and B 1 = √(14 - x₁)² + (10 - y₁)² 1 = 196 - 28x₁ + x₁² + 100 - 20y₁ + y₁² --> eqn 2
The last equation would be the linear equation using points A and B. m = (10-8)/(14-4) = 1/5 = (8 - y₁)/(4 - x₁) 4 - x₁ = 5(8 - y₁) 4 - x₁ = 40 - 5y₁ -36 = x₁ - 5y₁ --> eqn 4
Solve equations 3 and 4 simultaneously: x₁ = 9.38 y₁ = 9.08 Therefore, the closest answer is letter B.