jee-main 2024 Q66

jee-main · India · session1_31jan_shift2 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation

Let $A(a, b)$, $B(3, 4)$ and $(-6, -8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2a+3, 7b+5)$ from the line $2x + 3y - 4 = 0$ measured parallel to the line $x - 2y - 1 = 0$ is
(1) $\dfrac{15\sqrt{5}}{7}$
(2) $\dfrac{17\sqrt{5}}{6}$
(3) $\dfrac{17\sqrt{5}}{7}$
(4) $\dfrac{\sqrt{5}}{17}$

Let $A(a, b)$, $B(3, 4)$ and $(-6, -8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2a+3, 7b+5)$ from the line $2x + 3y - 4 = 0$ measured parallel to the line $x - 2y - 1 = 0$ is\\
(1) $\dfrac{15\sqrt{5}}{7}$\\
(2) $\dfrac{17\sqrt{5}}{6}$\\
(3) $\dfrac{17\sqrt{5}}{7}$\\
(4) $\dfrac{\sqrt{5}}{17}$

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