Question

Centroid of the triangle formed by points (7,p),(q,-6),(9,10) is (6,3) then write the value of (p+q).

Answer 1

The value of (p+q) is 7.

Step-by-step explanation:

The vertices of a triangle are (7,p), (q,-6), (9,10).

Formula for centroid  of a triangle:

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

where, $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are vertices of the triangle.

Centroid of given triangle is

$Centroid=(\dfrac{7+q+9}{3},\dfrac{p-6+10}{3})$

$Centroid=(\dfrac{16+q}{3},\dfrac{p+4}{3})$

It is given that centroid of given triangle is (6,3).

$(\dfrac{16+q}{3},\dfrac{p+4}{3})=(6,3)$

On comparing both sides we get

$\dfrac{16+q}{3}=6$

$16+q=18$

$q=18-16$

$q=2$

The value of q is 2.

$\dfrac{p+4}{3}=3$

$p+4=9$

$p=9-4$

$p=5$

The value of p is 5.

The value of p+q is

$p+q=5+2=7$

Therefore, the value of p+q is 7.

#Learn more

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Answer 2

Answer:

the anwer is 7

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