A , B and C are col-linear ⇒⇒⇒ ∴ slope of AB = slope of BC slope of AB = (2-8)/(7-4) = -2 slope of BC = (y-2)/(x-7) ∴ (y-2)/(x-7) = -2 ∴ (y-2) = -2 (x-7) ⇒⇒⇒ equation (1)
The distance
between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex]
The ratio of AB : BC = 3:2 AB/BC = 3/2 ∴ 2 AB = 3 BC [tex]2 * \sqrt{ (7-4)^{2} + (2-8)^{2} } [/tex] = [tex] 3* \sqrt{ (x-7)^{2} +(y-2)^{2} } [/tex] eliminating the roots by squaring the two side and simplifying the equation ∴ 4 * 45 = (x-7)² + (y-2)² ⇒⇒⇒ equation (2) substitute by (y-2) from equation (1) at equation (2) 4 * 45 = 5 (x-7)² solve for x ∴ x = 9 or x = 5 ∴ y = -2 or y = 6
The point will be (9,-2) or (5,6) the point (5,6) will be rejected because it is between A and B