if one diagonal of a square is the portion of the line x/a + y/b = 1 intercepted by the - Maths - Straight Lines

Question

if one diagonal of a square is the portion of the line x/a + y/b =
1 intercepted by the axes , then the extremities of the other
diagonal of the square are what?

Anuradha Sharma · Accepted Answer

The end points of the diagonal xa+yb=1 are, a,0 and 0,bTmid point is a2,b2Slop is tanθ=-baslope of other diagonal is tanα= abLet the angle made by other diagonal is αSo cosα=ba2+b2 and sinα=aa2+b2half the length of diagonal =12a2+b2The end point of the other diagonal are at a distance of 12a2+b2 from a2,b2 on a line of slope =abUsing displacement concept, The required end points area2+12a2+b2cosα, b2+12a2+b2sinα and a2-12a2+b2cosα, b2-12a2+b2sinα =a2+12a2+b2×ba2+b2, b2+12a2+b2×aa2+b2 and a2-12a2+b2×ba2+b2, b2-12a2+b2×aa2+b2=a+b2,a+b2 and a-b2,a-b2

if one diagonal of a square is the portion of the line x/a + y/b = 1 intercepted by the axes , then the extremities of the other diagonal of the square are what?