Question

ABC is a triangle. G(4,3) is centroid of triangle. If A,B,C are the points (1,3),(4,b),(a, 1) respectively find the value of a and b also find the length of side BC.. Plzzzzzz give full solution of it

Answer 1

using centroid formula we could obtain a and b
a=7,b=5

Answer 2

Answer:

The value of a is 7. The value of b is 5.The length of BC is 5 units.

Step-by-step explanation:

The vertices of a triangle are (1,3),(4,b),(a, 1).

The formula for centroid is

$Centroid=(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})$

The centroid of triangle is G(4,3).

$(4,3)=(\frac{1+4+a}{3}, \frac{3+b+1}{3})$

$(4,3)=(\frac{5+a}{3}, \frac{4+b}{3})$

Compare both sides.

$4=\frac{5+a}{3}$

$12=5+a$

$a=7$

The value of a is 7.

$3=\frac{4+b}{3}$

$9=4+b$

$b=5$

The value of b is 5.

The distance formula is

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of side BC is

$BC=\sqrt{(7-4)^2+(1-5)^2}=5$

Therefore the length of BC is 5 units.