If the distance of P(x,y) from A(5,1) and B(−1,5) are equal then pove that 3x=2y.
Three vertices of a rectangle ABCD are A(3,1),B(−3,−1) and C(−3,3). Plot these points on the graph paper and find the coordinates of the fourth vertex D. Also, find the area of the rectangle ABCD.
(Street plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city-run parallel to these roads and are 200m apart. There are 5 streets in each direction. Using 1 cm =200m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this conversion, find:(i) How many cross-streets can be referred to as (4,3)
(ii) How many cross-streets can be referred to as (3,4).
A(7,−3),B(5,3) and C(3,−1) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1),B(4,3) and C(2,5).