Question

Find K if (K,2 ) is an interior point of the triangle formed by the lines x+y=4, 3x-7y=8 and 4x-y=31.



Let ABC be the triangle then the coordinates of A, B, C are (8.36, 2.44), (7, –3), (3.6, 0.4). The point K (K, 2) will be inside ∆ABC if the following three conditions hold simultaneously.



(i)A and K lie on same side of BC

⇒ (8.36 + 2.44 – 4) (K + 2 – 4) > 0

⇒ 6.8 (K 0 – 2) > 0

⇒ K – 2 > 0

⇒ K > 2 .........(1)



(ii)B and K both lies on same side of AC

⇒ (3 × 7 – 7 (–3) –8) (3K – 7 × 2 – 8) > 0

⇒ 36 (3K – 14 – 8) > 0

⇒ 3K – 22 > 0

.........(2)



(iii) C and K both lies on the same side of AB

⇒ (4 × 3.6 – 0.4 – 31) (4K – 2 – 31) > 0

⇒ –14 (4K – 33) > 0

⇒ 4K – 33 < 0

........(3)



from (1), (2) and (3) we get



i can't understand why(8.36 + 2.44 – 4) (K + 2 – 4) > 0,
(3 × 7 – 7 (–3) –8) (3K – 7 × 2 – 8) > 0 ,
(4 × 3.6 – 0.4 – 31) (4K – 2 – 31) > 0 .

Answer 1

3...........is )A and K lie on same side of BC

⇒ (8.36 + 2.44 – 4) (K + 2 – 4) > 0

⇒ 6.8 (K 0 – 2) > 0

⇒ K – 2 > 0

⇒ K > 2 .........(1)

(ii)B and K both lies on same side of AC

⇒ (3 × 7 – 7 (–3) –8) (3K – 7 × 2 – 8) > 0

⇒ 36 (3K – 14 – 8) > 0

⇒ 3K – 22 > 0

.........(2)

(iii) C and K both lies on the same side of AB

⇒ (4 × 3.6 – 0.4 – 31) (4K – 2 – 31) > 0

⇒ –14 (4K – 33) > 0

⇒ 4K – 33 < 0

........(3)

from (1), (2) and (3) we get



i can't understand why(8.36 + 2.44 – 4) (K + 2 – 4) > 0,
(3 × 7 – 7 (–3) –8) (3K – 7 × 2 – 8) > 0 ,
(4 × 3.6 – 0.4 – 31) (4K – 2 – 31) > 0 .

Answer 2

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