Prove that any number for x the point $(x, 2 x + 3)$ is on the line joining $(- 1, 1), (2, 7)$ .

Open in App

Solution

let $(x, 2 x + 3)$ lie on the line joining points $(- 1, 1)$ and $(2, 7)$
when third point lie on line joining points then it form collinear line

$⎛ ⎜ ⎝ \begin{matrix} - 1 & 1 & 1 2 & 7 & 1 x & 2 x + 3 & 1 \end{matrix} ⎞ ⎟ ⎠ = 0$ [if 3 points are collinear then its determinats is]
$\Rightarrow - 1 (7 - 2 x - 3) - 1 (2 - x) + 1. (4 x + 6 - 7 x) = 0 \Rightarrow - 4 + 2 x - x - 2 + 4 x + 6 - 7 x = 0 \Rightarrow - 2 x + 0 = 0 \Rightarrow x = 0 (2 x + 3) = 3 p o i n t (0, 3)$
when third point $(0, 3)$ lie on line joining points $(- 1, 1)$ and $(2, 7)$ then it form collinear line

Suggest Corrections

Similar questions

Q. If

P (x, y)

is any point on the line segment joining the points

(a, 0)

and

(0, b)

then prove that

\frac{x}{a} + \frac{y}{b} = 1

If (x, y) be on the line joining the two points (1, -3) and (-4, 2), prove that x+ y+ 2 = 0.

Prove that for all points on the line joining the origin and the point (4, 2) the x-coordinates is double the y-coordinates. What is the equation of this line?

Q. The curve for which the normal at any point

(x, y)

and the line joining origin to that point form an isosceles triangle with x axis as base is

Join BYJU'S Learning Program

Prove that any number for x the point (x,2x+3) is on the line joining (−1,1),(2,7).

Prove that any number for x the point $(x, 2 x + 3)$ is on the line joining $(- 1, 1), (2, 7)$ .