Question

If area of triangle with vertices ( 2 , - 6 ), ( - 2 , 4 ) and ( k , 4 ) is 35, then k = ______​

Answer 1

Answer:

k = -9

Step-by-step explanation:

Area of a triangle whose vertices are (x₁,y₁),(x₂,y₂) & (x₃,y₃) is given by the formula A =  (1/2) [x₁ (y₂ – y₃ ) + x₂ (y₃ – y₁ ) + x₃(y₁ – y₂)] sq. units

here, having given the 3 vertices and area as (2,- 6), (- 2,4) ,(k,4) & 35 sq.units resply.

=> 35 = (1/2) [2 (4 – 4 ) + (-2) (4– (-6) ) + k((-6) – 4)]

=> 35 = (1/2) [ 0 -2(4+6) +k (-10) ]

=> 35*2 =  [-20-10k]

=> 70 +20 = -10k

=> 10 k = -90

=> k = -90/10

=> k = -9