If a triangle has its orthocenter at 1-1 and circumcenter at 3-2- 3-4- then the coordinates of the centroid of the triangle are

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Relation between O,G,C

If a triangle...

Question

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2}, \frac{3}{4})$ , then the coordinates of the centroid of the triangle are

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Solution

The correct option is B

Since the centroid divides the line joining the orthocenter and circumcenter in the ratio 2:1 internally,

Therefore, if the centroid is (x, y), then

$x = \frac{2. \frac{3}{2} + 1.1}{2 + 1} = \frac{4}{3} a n d y = \frac{2. \frac{3}{4} + 1.1}{2 + 1} = \frac{5}{6}$

$∴$ Coordinates of centroid are $(\frac{4}{3}, \frac{5}{6})$

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If a triangle has its orthocenter at (1, 1) and circumcenter at (32,34) , then the coordinates of the centroid of the triangle are

The correct option is B Since the centroid divides the line joining the orthocenter and circumcenter in the ratio 2:1 internally, Therefore, if the centroid is (x, y), then x=2.32+1.12+1=43 and y=2.34+1.12+1=56 ∴ Coordinates of centroid are (43,56)

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2}, \frac{3}{4})$ , then the coordinates of the centroid of the triangle are