Question

If coordinaters of vertices of triangle are $(3,-5)$ and $(-7,4)$ and its centroid is $(2,1)$. The coordinates of third vertex are

• A. $(10,4)$
• B. $(-10,4)$
• C. $(-10,-4)$
• D. $(10,-4)$

Answer 1

Answer: (A)

$(10,4)$

if $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are vertices of the triangle then

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

Do Let third vertex be $(x,y)$

So centroid is $(\frac{3-7+x}{3},\frac{-5+4+y}{3})=(2,1)$

$⟹x-4=6,y-1=3$

$⟹$ Third vertex is $(10,4)$