Find x so that the points (3,-2),(x,2)and (8,8) be on a line (ans is x=5) 2 For what value - Maths - Determinants

Question

Find x so that the points (3,-2),(x,2)and (8,8) be on a line
(ans is x=5)

2 For what value of k the points (5,5),(k,1)and(11,7)are
collinear(ans is k=-7)

Lalit Mehra · Accepted Answer

Let A(x1, y1), B(x2, y2) and C(x3, y3) be three point Then, A, B, C are collinear, if $\frac{1}{2} | \begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y 3 & 1 \end{matrix} | = 0 \Rightarrow | \begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{matrix} | = 0$ 1 The given point are (3, â€“ 2), (x, 2) and (8, 8) These point lie on a line So, they are collinear $∴ | \begin{matrix} 3 & - 2 & 1 \\ x & 2 & 1 \\ 8 & 8 & 1 \end{matrix} | = 0$ $\Rightarrow 3 (2 - 8) - (- 2) (x - 8) + 1 (8 x - 16) = 0 \Rightarrow - 18 + 2 x - 16 + 8 x - 16 = 0 \Rightarrow 10 x - 50 = 0 \Rightarrow 10 x = 50 \Rightarrow x = 5$ Thus, the value of x is 5 2 The given point are (5, 5), (k, 1) and (11, 7) are collinear $∴ | \begin{matrix} 5 & 5 & 1 \\ k & 1 & 1 \\ 11 & 7 & 1 \end{matrix} | = 0$ $\Rightarrow 5 (1 - 7) - 5 (k - 11) + 1 (7 k - 11) = 0 \Rightarrow - 30 - 5 k - 55 + 7 k - 11 = 0 \Rightarrow 2 k + 14 = 0 \Rightarrow 2 k = - 14 \Rightarrow k = - 7$ Thus, the value of k is â€“ 7

Find x so that the points (3,-2),(x,2)and (8,8) be on a line.(ans is x=5) 2.For what value of k the points (5,5),(k,1)and(11,7)are collinear(ans is k=-7)

Find x so that the points (3,-2),(x,2)and (8,8) be on a line.(ans is x=5)

2.For what value of k the points (5,5),(k,1)and(11,7)are collinear(ans is k=-7)