If the co-ordinates of orthocentre and the centroid of a triangle ABC are (–5, 7) and (5, 5), then the circumcentre of the triangle ABC is:
Explanation:
We know that Centroid divides the line joining the Orthocenter and Circumcenter in the ratio 2 : 1.
Let the coordinates of Circumcenter be(x, y) ∴ Orthocenter ((–5, 7)) ; Centroid (5, 5); Circumcenter (x, y). Using the section formula; 5 = (2x − 5)/3 ⇒ x = 10. 5 = (2y + 7)/3 ⇒ y = 4. So, the coordinates of the circum-center are (10, 4). Hence option (b).
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