Question

If (a, b) be an end of a diagonal of a square and the other diagonal has the equation `x-y=a`, then another vertex of the square can be
A. `(a-b,a)`
B. `(a,0)`
C. `(0,-a)`
D. `(a+b,b)`

Answer 1

Correct Answer - B::D

Diagonal AC is `x - y = a`
`:.` Slope `BD =- 1`
Also BD passes through (a,b)
`:.` Equation of BD is `x +y = a+b`
Solving, we get point `O -= (a+(b)/(2),(b)/(2))`
`:.` point `B -= (a+b,0)`
`m_(AC) = 1 = tan theta`
`OA = OD = (b)/(sqrt(2))`
Using parametric form of straight line points A and C are given by
`(a+(b)/(2)+-(b)/(sqrt(2))cos 45^(@),(b)/(2)+-(b)/(sqrt(2))sin45^(@))`
or `A(a,0)` and `C(a+b,b)`