The equation of two sides of a triangle are 3x+4y-12=0,2x+y-8=0. If the circumcentre is (0 , 3), then the centroid of the triangle is

Question

The equation of two sides of a triangle are 3x+4y-12=0,2x+y-8=0. If the circumcentre is (0 , 3), then the centroid of the triangle is (A) (0 , (7/3)) (B) (0 , (14/3)) (C) (0 , (16/3)) (D) (0 , 6)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-nnzvnnuqz4fyiehh.jpg" /> Foot of perpendicular from (0 , 3) on the line 2x+y-8=0 is (2 , 4) Hence, P is (0 , 8) which is orthocentre ∴ Centroid is (0 , (14/3))

Q. The equation of two sides of a triangle are $3 x + 4 y - 12 = 0, 2 x + y - 8 = 0.$ If the circumcentre is $(0, 3),$ then the centroid of the triangle is

$(0, \frac{7}{3})$

$(0, \frac{14}{3})$

$(0, \frac{16}{3})$

$(0, 6)$

Foot of perpendicular from $(0, 3)$ on the line
$2 x + y - 8 = 0$ is $(2, 4)$
Hence, $P$ is $(0, 8)$ which is orthocentre
$∴$ Centroid is $(0, \frac{14}{3})$

Q. The equation of two sides of a triangle are 3x+4y−12=0,2x+y−8=0. If the circumcentre is (0,3), then the centroid of the triangle is

(0,37​)

(0,314​)

(0,316​)

(0,6)