The distance of the point (2,3) from the line 2 x-3 y+9=0 measured along a line x-y+1=0 is :

Question

The distance of the point (2,3) from the line 2 x-3 y+9=0 measured along a line x-y+1=0 is : (A) 5 √3 (B) 4 √2 (C) 3 √2 (D) 2 √2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/65cf4d83a3606d349322b9550a15aa6a-.png" /> Let coordinates of point P by parametric form P(2+r cos 45°, 3+r sin 45°) It satisfies the line 2 x-3 y+9=0 ∴ 2(2+(r/√2))-3(3+(r/√2))+9=0 ⇒ r=4 √2

Q. The distance of the point $(2, 3)$ from the line $2 x - 3 y + 9 = 0$ measured along a line $x - y + 1 = 0$ is :

$53$

$42$

$32$

$22$

Let coordinates of point $P$ by parametric form
$P (2 + r cos 4 5^{\circ}, 3 + r sin 4 5^{\circ})$
It satisfies the line $2 x - 3 y + 9 = 0$
$∴ 2 (2 + \frac{r}{2}) - 3 (3 + \frac{r}{2}) + 9 = 0$
$\Rightarrow r = 42$

Q. The distance of the point (2,3) from the line 2x−3y+9=0 measured along a line x−y+1=0 is :

53​

42​

32​

22​