CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If the orthocentre, circumcentre of a triangle are $$(-3,5,2),(6,2,5)$$ respectively, then the centroid of the triangle is


A
(3,3,4)
loader
B
(32,72,92)
loader
C
(9,9,12)
loader
D
(92,32,32)
loader

Solution

The correct option is A $$(3,3,4)$$
Circumcentre $$= \left( 6, 2, 5 \right)$$
Orthocenter $$= \left( -3, 5 , 2 \right)$$
As we know that centroid divides the line joining orthocentre and circumcentre in ratio $$2 : 1$$.
Therefore, on applying section formula,
Centroid $$= \left( \cfrac{1 \times \left( -3 \right) + 2 \times 6}{2 + 1}, \cfrac{1 \times 5 + 2 \times 2}{2 + 1}, \cfrac{1 \times 2 + 2 \times 5}{2 + 1} \right) \\ = \left( \cfrac{-3 + 12}{3}, \cfrac{5 + 4}{3}, \cfrac{2 + 10}{3} \right) \\ = \left( 3, 3, 4 \right)$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image