Using determinants show that the following points are collinear: … - Vidyadip

Question

Using determinants show that the following points are collinear:
(5, 5), (-5, 1) and (10, 7)

✓

Answer

If 3 points are collinear, then the area of the triangle then form will be zero.
Hence, $\frac{1}{2}\begin{vmatrix}5&5&1\\-5&1&1\\10&7&1\end{vmatrix}=0$
Expanding along R₁
$=\frac{1}{2}\big[5(-6)-5(-15)+1(-35-10)]$
$=\frac{1}{2}[-35+75-45]$
$=\frac{1}{2}[0]$
$=0$
Since the area of the triangle is zero, hence the points are collinear.

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 "3 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

For each of the differential equations in find a particular solution satisfying the given condition:
$\text{cos}\bigg(\frac{\text{dy}}{\text{dx}}\bigg) = \text{a}(\text{a} \in \text{R}); \ \text{y}=1\text{when x = }0$

Integrate the function: $\frac{{2\cos x - 3\sin x}}{{6\cos x + 4\sin x}}$

Evaluate the following determinant:
$\begin{vmatrix}\cos15^\circ&\sin15^\circ\\\sin75^\circ&\cos75^\circ \end{vmatrix}$

A bag contains 8 red and 6 green balls. Three balls are drawn one after another without replacement. Find the probability that at least two balls drawn are green.

If y = cos^-1x. Find $\frac{{{d^2}y}}{{d{x^2}}}$ in terms of y alone.

Write the coordinates of the point at which the tangent to the curve y = 2x² - x + 1 is parallel to the line y = 3x + 9.

Find the value of k, for which $\text{f}(\text{x}) = $ $ \begin{matrix} \frac{\sqrt{1 + \text{kx}} - \sqrt{1 - \text{kx}}}{\text{x}} , \text{if} - 1\leq\text{x} < 0\\ \frac{2\text{x} + 1}{\text{x} - 1} , \text{ if}0\leq\text{x}< 1 \end{matrix} $ is continuous at x = 0.

Evaluate the integral $\int_{0}^{2} x \sqrt{x+2}$ (Put x + 2 =t²) using substitution.

Let A = {1, 2, 3}. Write all one-one from A to itself.

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are collinear.