Question

In Figure, if line $l$ has a slope of $1$ and passes through the origin, which of the following points has $(x,y)$ coordinate such that $\frac{x}{y}>1$?

• A. A
• B. B
• C. C
• D. D
• E. E

Answer 1

The correct option is E E

Let coordinates of point $A(-x,y)$

Position of point w.r. to line given $x=y$

$-x=y\Rightarrow \frac{-x}{y}<0$

Point A is not satisfying the condition $\frac{x}{y}>1$

Let coordinates of point $B(x,y)$ where $y>x$

Position of point w.r. to line given $x=y$

$x=y\Rightarrow \frac{x}{y}<1$ becuase $y>x$

Point B is not satisfying the condition $\frac{x}{y}>1$

Let coordinates of point $C(x,-y)$

Position of point w.r. to line given $x=y$

$x=-y\Rightarrow \frac{-x}{y}<0$

Point C is not satisfying the condition $\frac{x}{y}>1$

Let coordinates of point $D(-x,-y)$ where $y>x$

Position of point w.r. to line given $x=y$

$-x=-y\Rightarrow \frac{x}{y}<1$ because $y>x$

Point D is not satisfying the condition $\frac{x}{y}>1$

Let coordinates of point $E(-x,-y)$ where $x>y$

Position of point w.r. to line given $x=y$

$-x=-y\Rightarrow \frac{x}{y}>1$

Point E is satisfying the condition $\frac{x}{y}>1$