ABC is a triangle G is the centroid D is the mid- point of BC. If A - (2, 3) and G = (7, 5), then the point D is

Question

ABC is a triangle G is the centroid D is the mid- point of BC. If A - (2, 3) and G = (7, 5), then the point D is (A)  ( (19/2),6) (B)  ( (9/2),4) (C) (8, (13/2)) (D)  ( (11/2),(11/2))

Tardigrade Admin · Accepted Answer

Since, D is the mid point of BC. So, coordinate of

BC

are

(\frac{x _{2} + x _{3}}{2}, \frac{y _{2} + y _{3}}{2})

Given,

G (7, 5)

is the centroid of

Δ A BC

∴ 7 = \frac{2 + x _{2} + x _{3}}{3}

and

5 = \frac{3 + y _{2} + y _{3}}{3}

\Rightarrow x_{2} + x_{3} = 21 - 2

and

y_{2} + y_{3} = 15 - 3

\Rightarrow x_{2} + x_{3} = 19

and

y_{2} + y_{3} = 12

\Rightarrow \frac{x _{2} + x _{3}}{2} = \frac{19}{2}

and

\frac{y _{2} + y _{3}}{2} = 6

∴

Coordinate of D are

(\frac{19}{2}, 6)

Q. $A BC$ is a triangle $G$ is the centroid $D$ is the mid- point of $BC$ . If $A - (2, 3)$ and $G = (7, 5)$ , then the point $D$ is

$(\frac{19}{2}, 6)$

$(\frac{9}{2}, 4)$

$(8, \frac{13}{2})$

$(\frac{11}{2}, \frac{11}{2})$

Q. ABC is a triangle G is the centroid D is the mid- point of BC. If A−(2,3) and G=(7,5), then the point D is

(219​,6)

(29​,4)

(8,213​)

(211​,211​)

Q. $A BC$ is a triangle $G$ is the centroid $D$ is the mid- point of $BC$ . If $A - (2, 3)$ and $G = (7, 5)$ , then the point $D$ is

$(\frac{19}{2}, 6)$

$(\frac{9}{2}, 4)$

$(8, \frac{13}{2})$

$(\frac{11}{2}, \frac{11}{2})$