The lien `x/3+y/4=1` meets the `y-` and `x-a x y s` at `Aa n dB` , respectively. A square `A B C D` is constructed on the line segment `A B` away from the origin. The coordinates of the vertex of the square farthest from the origin are (7, 3) (b) (4, 7) (c) (6, 4) (d) (3, 8)

Options

A. 7,3
B. 4,7
C. 6,4
D. 3,8

Answer

B

Explanation

The coordinates of A are (0,4) and those of B are (3,0).
`BC=AB=sqrt(3^(2)+4^(2)) = 5`
`"or " BL=BC "sin" theta "and " CL=BC "cos" theta`
`"or " BL=5 xx (4)/(5) = 4 "and"`
`CL=5 xx (3)/(5) = 3`
Similarly, MD =4 and AM=3.
So, the coordinates of C are (OB+BL,CL) `-=(7,3)` and those of D are (MD, OA+AM) `-=(4,7)`.
The coordinates of the vertex farthest from the origin are (4,7).