Find the coordinates of the point equidistant from three given points A(5,3),B(5,−5) and C(1,−5).
Find the ratio in which the line segment joining A(1, 5) and B(4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
A man starts from the point P(−3,4) and reaches the point Q(0,1) touching the x-axis at R(α,0) such that PR+RQ is minimum. Then 5∣α∣ (A) 3 (B) 5 (C) 4 (D) 2
In which quadrant or on which axis do each of the points (2, 4), (3, 1), (1, 0),(1,2) and (3,5)lie? Verify your answer by locating them on the Cartesian plane.
Prove that the circumcenter, orthocentre, incenter, and centroid of the triangle formed by the points A(−1,11),B(−9,−8), and C(15,−2) are collinear, without actually finding any of them.
Which of the following sets of points form an equilateral triangle? (1,0),(4,0),(7,−1) (0,0),(23,34),(34,23) (32,),(0,32),(1,1) (d) None of these
If P divides OA internally in the ratio λ1:λ2 and Q divides OA externally in the ratio λ1;λ2, then prove that OA is the harmonic mean of OP and OQ˙