Question

If (3,0),(2,a) and (b,6) are the vertices of a triangle ABC whose centroid is (2,5).Find the values of a and b.

Answer 1

Answer:

9,1

Step-by-step explanation:

$\displaystyle \text{Centroid is given by } \left(\frac{x_1 + x_2 + x_3 }{3}, \frac{y_1 + y_2 + y_3 }{3}\right)\\\\\therefore \frac{3+2+b}{3} = 2, \frac{0+a+6}{3} = 5$

On solving we get a = 9 and b = 1.

Answer 2

The value of a = 9 , b = 1

Given :

(3,0),(2,a) and (b,6) are the vertices of a triangle ABC whose centroid is (2,5).

To find :

The values of a and b.

Formula :

If ( x₁ , y₁) , (x₂ , y₂) & (x₃ , y₃) are three vertices of a triangle then the centroid of the triangle is given by

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2+ x_3}{3} , \frac{y_1 + y_2+y_3}{3} \bigg)}$

Solution :

Step 1 of 2 :

Form the equation to find the value of a and b

Here it is given that (3,0),(2,a) and (b,6) are the vertices of a triangle ABC

∴ The centroid of the triangle is

$\displaystyle \sf{ = \bigg( \frac{3 + 2 + b}{3} , \frac{0 + a + 6}{3} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{ b + 5}{3} , \frac{ a + 6}{3} \bigg)}$

By the given condition

$\displaystyle \sf{ \bigg( \frac{ b + 5}{3} , \frac{ a + 6}{3} \bigg) = (2, 5)}$

Thus we get

$\displaystyle \sf{ \frac{ b + 5}{3} = 2 \: \: \: and \: \: \frac{ a + 6}{3} = 5}$

Step 2 of 2 :

Find the value of a and b

$\displaystyle \sf{ \frac{ b + 53} = 2 \: \: \: and \: \: \frac{ a + 6}{3} = 5}$

Now ,

$\displaystyle \sf{ \frac{ b + 5}{3} = 2}$

$\displaystyle \sf{ \implies \: b = 6 - 5}$

$\displaystyle \sf{ \implies \: b = 1}$

Again ,

$\displaystyle \sf{ \frac{ a + 6}{3} = 5}$

$\displaystyle \sf{ \implies a + 6 = 15}$

$\displaystyle \sf{ \implies a = 15 - 6}$

$\displaystyle \sf{ \implies a = 9}$

Hence the required value of a = 9 , b = 1

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ locate the following points on the cartesian plane(aEr) (0,a),(a,0),(-a, 0),(0,-a)

https://brainly.in/question/26822338

2. On a coordinate grid, the location of a bank is (–4, 8) and the location of a post office is (2, 0).

https://brainly.in/question/23287117

#SPJ3