If the points (x, -2), (5, 2), (8, 8) are collinear, find x using… - Vidyadip

Question

If the points (x, -2), (5, 2), (8, 8) are collinear, find x using determinants.

✓

Answer

The points (k, -2), (5, 2), (8, 8) are collinear.
$\begin{vmatrix}\text{x}&-2&1\\5&2&1\\8&8&1\end{vmatrix}=0$
$\triangle=\begin{vmatrix}\text{x}&-2&1\\5&2&1\\8&8&1\end{vmatrix}$
$=\begin{vmatrix}\text{x}&-2&1\\5-\text{x}&4&0\\8&8&1\end{vmatrix}$ [Applying R₂ → R₂ - R₁]
$=\begin{vmatrix}\text{x}&-2&1\\5-\text{x}&4&0\\8-\text{x}&10&0\end{vmatrix}$ [Applying R₃ → R₃ - R₁]
$=\begin{vmatrix}5-\text{x}&4\\8-\text{x}&10\end{vmatrix}$
$=50-10\text{x}-32+4\text{x}$
$=18-6\text{x}=0$
$\Rightarrow\text{x}=3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\frac{\text{x}\sin\text{x}\cos\text{x}}{\sin^4\text{x}+\cos^4\text{x}}\text{ dx}$

If $\text{y}=(\cot^{-1}\text{x})^2$ prove that $\text{y}^2(\text{x}^2+1)^2+2\text{x}(\text{x}^2+1)\text{y}_1=2.$

Find $\frac{\text{dy}}{\text{dx}}$ of the functions expressed in parametric:
$\text{x}=\frac{1+\log\text{t}}{\text{t}^2},\text{ y}=\frac{3+2\log\text{t}}{\text{t}}.$

If $\text{A}=\begin{bmatrix}2&-1\\3&2 \end{bmatrix} $ and $\text{B}=\begin{bmatrix}0&4\\-1&7\end{bmatrix} ,$ find 3A² - 2B + l

Find the value of 'a' for which the function f defined by
$\text{f}\text{(x)}=\begin{cases}\text{a}\sin\frac{\pi}{2}(\text{x}+1),& \text{x}\leq0 \\\frac{\tan\text{x-sin}\text{x}}{\text{x}^3} &\text{x} > 0\end{cases}$ is discontinuous at x = 0.

A straight line is drawn through a given point P(1, 4). Determine the least value of the sum of the intercepts on the coordinate axes.

Solve the following systems of linear equations by cramer's rule:

Find the particular solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{xy}}{\text{x}^2+\text{y}^2}$ given that y = 1 when x = 0.

A chemical company produces two compounds, A and B. The following table gives the units of ingredients, C and D per kg of compounds A and B as well as minimum requirements of C and D and costs per kg of A and B. Find the quantities of A and B which would give a supply of C and D at a minimum cost.

	Compound		Minimum requirement
	A	B
Ingredient C	1	2	80
Ingredient D	3	1	75
Coist (in Rs.) per Kg	4	6

Verify Rolle's theorem of the following function on the indicated interval
$\text{f}(\text{x})=2\sin\text{x}+\sin2\text{x}\text{ on }[0,\pi]$