A triangle has vertices at A(0, 0), B(6, 0), and C(0, 8). What are the coordinates of its Circumcenter?
(3, 4)
AB lies on the x-axis and AC lies on the y-axis, so the angle at A is 90°.
In a right-angled triangle the circumcentre is the midpoint of the hypotenuse, here BC.
Midpoint of B(6, 0) and C(0, 8) = \(\left(\frac{6+0}{2}, \frac{0+8}{2}\right) = (3, 4)\).
Hence, the circumcentre is (3, 4).
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In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
A1 (x1, y1), A2 (x2, y2), A3 (x3, y3) and A4 (x4, y4) are 4 points, p1 divides A1A2 in the ratio 1 ∶ 1, p2 divides P1A3 in the ratio 1 ∶ 2, P3 divides p2A4 in the ratio 1 ∶ 3. Then the coordinates of p3 are:
The polar coordinates of the vertices of a triangle are (0, 0), \(\left( {3,\frac{\pi }{2}} \right)\) and \(\left( {3,\frac{\pi }{6}} \right)\). Then, the triangle is:
