Question

The equation of a graph is given as $x=0.5y$
The points satisfying the given equation are .

• A. A = (0,0)
  B = (1,4)
• B. A = (0,0)
  B = (4,1)
• C. A = (1,2)
  B = (2,4)
• D. A = (2,1)
  B = (4,2)

Answer 1

The correct option is C A = (1,2)

B = (2,4)
The given equation is,
$x=0.5y$
$\Rightarrow \text{y}=\frac{1}{0.5}x$
$\Rightarrow \text{y}=2x$

Now, putting the coordinates of the points A and B in the equation $y=2x$.

Given coordinates of Point A are (0,0), (1, 2), and (2, 1).

Considering the options for Point A, we get,
$\text{When}\text{x}=0,\text{y}=2\times 0=0\Rightarrow$ (0,0)
$\text{When}\text{x}=1,\text{y}=2\times 1=2\Rightarrow$ (1,2)
$\text{When}\text{x}=2,\text{y}=2\times 2=4\Rightarrow$ (2,4

∴ Point A can be either (0,0) or (1,2).



Now, coordinates of Point B are given as (2,4), (4,2), (1,4) and (4,1).

Considering the options for Point B, we get,
$\text{When}\text{x}=2,\text{y}=2\times 2=4\Rightarrow (2,4)$
$\text{When}\text{x}=4,\text{y}=2\times 4=8\Rightarrow (4,8)$
$\text{When}\text{x}=1,\text{y}=2\times 1=2\Rightarrow (1,2)$

∴ Point B is (2,4).


So, Point A (1,2) and Point B (2,4) lie on the equation $y=2x$.