If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie o...
If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t.
t = -2 and 3
t = 2 and -3
t = 2 and 3
t = -2 and -3
Correct answer is C
For collinear points (points on the same line), the slopes are equal for any 2 points on the line.
Given (-1, t - 1), (t, t - 3), (t - 6, 3),
\(slope = \frac{(t-3) - (t-1)}{t - (-1)} = \frac{3 - (t-3)}{(t-6) - t} = \frac{3 - (t-1)}{(t-6) - (-1)}\)
Taking any two of the equations above, solve for t.
\(\frac{t - 3 - t + 1}{t + 1} = \frac{6 -t}{-6}\)
\(12 = (6 - t)(t + 1)\)
\(-t^{2} + 5t + 6 - 12 = 0 \implies t^{2} - 5t + 6 = 0\)
Solving, we have t = 2 and 3.
Evaluate \(\cos 75°\), leaving the answer in surd form....
Marks 5 - 7 8 - 10 11 - 13 14 - 16 17 - 19 20 - 22 Frequency 4 7 26 41 1...
If \(P = \begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} -2 & ...
Find the minimum value of \(y = x^{2} + 6x - 12\)....
Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?...