Q. 245.0( 3 Votes )

The point A divides the join of P ( - 5, 1) and Q (3, 5) in the ratio k: 1. Find the two values of k for which the area of Δ ABC where B is (1, 5) and C (7, - 2) is equal to 2 units.

Answer :

Given: Area ΔABC = 2 units


To find: The value of k.


Formula Used:


section formula:


If point P (x, y) divides the line segment A (x1, y1) and B(x2,y2)


Then the coordinates of P are:



Area of the triangle having vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃)
= 1/2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |


Explanation:


coordinates A can be given by using section formula for internal division,


A


and B (1,5), C (7, −2)


Area of ∆ABC



But Area ∆ABC = 2



Solving above we get,



Taking positive sign, 14k 66 = 4k + 4


10k = 70


k = 7


Taking negative sign, we get,


14k 66 = 4k 4


18k = 62



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