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 $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$ measured parallel to the line $x-2 y-1=0$ is
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 $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$ measured parallel to the line $x-2 y-1=0$ is
- [JEE MAIN 2024]
- A
$\frac{15 \sqrt{5}}{7}$
- B
$\frac{17 \sqrt{5}}{6}$
- C
$\frac{17 \sqrt{5}}{7}$
- D
$\frac{\sqrt{5}}{17}$
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