Show that the following points are collinear.
A(−5,1),B(5,5) and C(10,7).
In ABC, if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of ABC) is (21,32) (b) (31,32) (32,1) (d) none of these
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, 3) and B is (1, 4).
Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of ΔABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe?
(v) If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of ∆ ABC, find the coordinates of the centroid of the triangle.
If )−4,0) and (1,−1) are two vertices of a triangle of area 4squ˙nits, then its third vertex lies on y=x (b) 5x+y+12=0 x+5y−4=0 (d) x+5y+12=0
Find the coordinates of the point which divides the line segment joining the points (4, 3) and (8, 5)in the ratio 3 : 1 internally.
Figure shows the arrangement of desks in a classroom Ashima, Bharti and Camella are seated at A(3, 1), B(6, 4) and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer.