Question

the coordinates of vertex A of Triangle ABC are(-4,2) and point D (2,5),D is a mid point BC,the coordinates of c centroid of a triangle are​

Answer 1

Step-by-step explanation:

Given:The coordinates of vertex A of Triangle ABC are(-4,2) and point D (2,5),D is a mid point BC.

To find:Coordinates of c centroid of a triangle.

Solution: The centroid of triangle is lies at a distance of 2:1 of the median.

If we join median AD(Since D is midpoint of BC),

so centroid of triangle is at 2:1 on median.

Apply section formula:

Let c(x,y)

$\bold{x = \frac{mx_1 + nx_2}{m + n}} \\ \\ \bold{y = \frac{my_1 + ny_2}{m + n}}$

here A(-4,2)

D(2,5)

ratio= 2:1

$x = \frac{2 \times 2 + 1 \times ( - 4)}{2 + 1} \\ \\x = \frac{4 - 4}{3} \\ \\ x = \frac{0}{3} \\ \\ x = 0 \\ \\ y = \frac{2 \times 5 + 1 \times2}{2 + 1} \\ \\ y = \frac{12}{3} \\ \\ y = 4$

Coordinates of centroid are (0,4).

Option A is correct.

Hope it helps you.

To learn more on brainly:

1)if A(-3,5),B(-1,1)and c(3,3) are the vertices of a triangle ABC,find the length of median AD.Also find the co- ordinates...

https://brainly.in/question/2007696

2)Find the coordinates of the centroid of a triangle whose vertices are (0 6) (8 12) and (8 0)

https://brainly.in/question/2072149

Answer 2

Answer:

Option A is correct.........