In Fig. 3, the area of triangle ABC (in sq. units) is :
If (1,4) is the centroid of a triangle and the coordinates of its any two vertices are (4,−8) and (−9,7), find the area of the triangle.
If A(x1,y1),B(x2,y2), and C(x3,y3) are three non-collinear points such that x12+y12=x22+y22=x32+y32, then prove that x1sin2A+x2sin2B+x3sin2C=y1sin2A+y2sin2B+y3sin2C=0.
If x1,x2,x3 as well as y1,y2,y3 are in GP with the same common ratio, then the points (x1,y1),(x2,y2), and (x3,y3)˙ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.
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.
Find the coordinates of the point which divides the line segments joining the points (6,3) and (−4,5) in the ratio 3:2 (i) internally and (ii) externally.
AB is a variable line sliding between the coordinate axes in such a way that A lies on the x-axis and B lies on the y-axis. If P is a variable point on AB such that PA=b,Pb=a , and AB=a+b, find the equation of the locus of P˙