If the points A(4,3) and B(x,5) lie on the circle with centre O(2,3), find the value of x.
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 points which divide the line segment joining A(−2,2) and B(2,8) into four equal parts.
OPQR is a square and M,N are the midpoints of the sides PQ and QR , respectively. If the ratio of the area of the square to that of triangle OMN is λ:6, then 4λ is equal to 2 (b) 4 (c) 2 (d) 16
The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of ΔPQR if C is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?