Question

AC has endpoints with coordinates A(−5,2) and C(4,−10). If B is a point on AC and AB:BC = 1:2, what are the coordinates of B?

Answer 1

Answer:

B(x, y) = (-2, -2)

Step-by-step explanation:

Given: AB: AC (m₁: m₂) = 1 : 2, A (x₁, y₁) = (-5, 2) and B(x₂, y₂) = (4, -10)

To find: Coordinates of B (x, y)

Using section formula:

$x = \frac{m_1x_2+ m_2x_1}{m_1 + m_2}\ and\ y = \frac{m_1y_2+ m_2y_1}{m_1 + m_2}$

∴ $x = \frac{(1\times 4) + (2\times(-5))}{1 + 2} = \frac{4 - 10}{3} = \frac{-6}{3} = -2$

and $x = \frac{(1\times (-10)) + (2\times 2)}{1 + 2} = \frac{-10 + 4}{3} = \frac{-6}{3} = -2$

Therefore Coordinates of B (x, y) is (-2, -2).