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

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Solution

$A (x, y)$ lies on line PB where $P (1, - 3)$ and $B (- 4, 2)$
IF P,B,A are on same line ->they are collinear
$=> \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y 1 & - 3 - 4 & 2 x & y \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = 0 => - 3 x - y - 10 - 4 y - 2 x = 0 => x + y + 2 = 0$

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

A(x,y) lies on line PB where P(1,−3) and B(−4,2)IF P,B,A are on same line ->they are collinear=>12∣∣ ∣ ∣ ∣∣xy1−3−42xy∣∣ ∣ ∣ ∣∣=0=>−3x−y−10−4y−2x=0=>x+y+2=0

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

$A (x, y)$ lies on line PB where $P (1, - 3)$ and $B (- 4, 2)$
IF P,B,A are on same line ->they are collinear
$=> \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y 1 & - 3 - 4 & 2 x & y \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = 0 => - 3 x - y - 10 - 4 y - 2 x = 0 => x + y + 2 = 0$