Question

Find the value of k, by using area of triangle formula, if the points
A(k +1,2k), B(3k, 2k + 3) and C (5k - 1,5k) are collinear.​

Answer 1

Step-by-step explanation:

• 0 = 1/2[(k + 1 )(2k + 3 - 5k) + 3k(5k - 2k) + (5k-1)(2k - 2k - 3)
• 0 = (k + 1)(3 - 3k) + 3k(3k) + (5k - 1)(-3)
• 0 = 3k - 3k*2 + 3 - 3k + 9k*2 - 15k +3
• 0 = 6k*2 - 15k + 6
• 0 = 2k*2 - 5k + 2
• 0 = 2k*2 - 4k - k + 2
• 0 = 2k(k -2) -1(k -2)
• 0 = (2k - 1)(k - 2)
• 2k - 1 = 0
• k = 1/2
• (OR)
• k - 2 = 0
• k = 2
• Therefore, value of'k' is 2