Find the point of the x-axis which is equidistant from (2,−5) and (−2,9).
Find the area of rhombus if its vertices are (3,0),(4,5),(−1,4) and (−2,−1) taken in order.
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q(1/2.q). Find the value of p and q.
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?
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7). Also find the value of y