The points (1,3),(5,1) are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2 x+c , then one of the vertex on the other diagonal is

Step-by-step solution

Diagonals of rectangle bisect each other. Midpoint of (1,3) and (5,1) is (3,2) . Also, y=2 x+ c passes through (3,2) . array rlrl & 2 & =2(3)+c & & c & =-4 array Other two vertices lie on y=2 x-4 . Let co-ordinates of B be (x, y) i.e., (x, 2 x-4) slope of AB slope of BC =-1 aligned & ( 2 x-4-3 x-1 ) ( 2 x-4-1 x-5 )=-1 & ( 2 x-7 x-1 ) ( 2 x-5 x-5 )=-1 & x^2-6 x+8=0 & x=4,2 aligned When x=4, y=4 When x=2, y=0 Vertex of the other diagonal is (2,0) .