Question

10. If A(-1, 0), B(5, -2) and C(8, 2) are the vertices of a ∆ABC then its centroid is

a) (12, 0) b) (6, 0) c) (0, 6) d) (4, 0)​

Answer 1

Step-by-step explanation:

If (x1,x2) (y1,y2) &(x3,y3) are vertices of a triangle then,

centroide of a triangle is given by the formula,

X = (x1+x2+x3)/3 &Y=(y1+y2+y3)/3

=> X = (-1+5+8)/3=4

& Y =(0-2+2)/3=0

Hence centroid of triangle (X,Y)=(4,0)

Ans. d) (4,0)

I hope,It was useful to you

Answer 2

$\underline{ \huge\bf\red{QuestiØn} :}$

Given :-

A triangle (Δ) ABC which has the following coordinates :

• A ( - 1 , 0 )

• B ( 5 , - 2 )

• C ( 8 , 2 )

Find :-

• Centroid of ΔABC

$\underline{ \: \huge\bf\green{SolutiØn} \: :}$

• A $( x_1 , y_1)$ ≡ A ( - 1 , 0 )

• B $( x_2 , y_2)$ ≡ B ( 5 , - 2 )

• C $( x_3 , y_3)$ ≡ C ( 8 , 2 )

Now, we know that :

$\begin{aligned}& \sf \qquad centroid \\ \\ & = ( \frac{x_1 + y_1 + z_1}{3} , \frac{x_2 + y_2 + z_2}{3} ) \\ \\ & = ( \frac{ - 1 + 5 + 8}{3} , \frac{0 - 2 + 2}{3} ) \\ \\ & = ( \frac{12}{3} , \frac{0}{3} ) \\ \\ & = ( \frac{ \cancel{12} \ {}^{4} }{ \cancel{3} \ _1 } , 0) \\ \\ & = ( 4 \: , 0) \end{aligned}$

Hence,

The coordinates the Centroid of the ΔABC is G ( 4 , 0 ) . [ option (d) ]

$\red{\rule{5.8cm}{0.02cm}}$

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$