For what value of k(k>0) is the area of the triangle with vertices (−2,5),(k,−4) and (2k+1,10) equal to 53 square units?
The points (−a,−b),(a,b),(a2,ab) are (a) vertices of an equilateral triangle (b) vertices of a right angled triangle (c) vertices of an isosceles triangle (d) collinear
The coordinates of A,B,C are (6,3),(−3,5),(4,−2) , respectively, and P is any point (x,y) . Show that the ratio of the area of PBC to that of ABC is 7∣x+y−2∣˙
The vertices A and D of square ABCD lie on the positive sides of x− and y−aξs, respectively. If the vertex C is the point (12,17) , then the coordinates of vertex B are (14,16) (b) (15, 3) 17,5) (d) (17,12)
If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2+1,a2+1) and (2a,−2a), then find the orthocentre.
A line cuts the x-axis at A(7,0) and the y-axis at B(0,−5) A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R
The three points (−2,2)(9,−2),and(−4,−3) are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these