If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k
Quadratic Equations (10)If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.
Answer
Points A, B and C are collinear. Therefore,
$\frac{1}{2}$ [(k +1)(2k 3 – 5k) 3k(5k – 2k) (5k – 1)(2k – 2k – 3)] = 0
= (k + 1)(3 – 3k) + 9k2 – 3(5k – 1) = 0
= 2k2 – 5k + 2 = 0
= (k - 2)(2k - 1) = 0
k = 2, $\frac{1}{2}$
Exam Year:
2017
Related Questions
- Find the roots of the quadratic equation $x^2 − x − 2 = 0 $
- Assertion (A): If one root of the quadratic equation $4x^2 − 10x + (k − 4) = 0$
- Find the nature of roots of the quadratic equation $2x^2 – 4x + 3 = 0$
- Which of the following is not a quadratic equation
- A quadratic polynomial the sum and product of whose zeroes are -3 and 2 respectively, is
- Solve for x: $\frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4$