Question

The variable length of the line segment $\text{AB}$ is given by $(x+2y+4)$ units. Select the correct pairs of $(x,y)$ which give the line segment's length as $10$ units.

• A. $(2,1),(6,-1),(-2,4)$
• B. $(2,1),(6,-1),(2,4)$
• C. $(2,1),(0,3),(2,4)$
• D. $(6,0),(2,1),(-2,4)$

Answer 1

The correct option is B $(2,1),(6,-1),(2,4)$

Given length : $x+2y+4$ units
$\Rightarrow$Let's take $x=2,y=1$
Then
$x+2y+4=2+1\times 2+4$
$=4+2+4$
$=10$ units.
$\Rightarrow$Let's take $x=6,y=-1$
Then
$x+2y+4=6+2\times -1+4$
$=6-2+4$
$=10$ units.
$\Rightarrow$Let's take $x=-2,y=4$
Then
$x+2y+4=-2+2\times 4+4$
$=-4+8+4$
$=10$ units.
and so on.