Question

Choose the correct statements.

• A. Equation of AC is $2y=x$
• B. Equation of BD is $y=x-2$
• C. The point of intersection of both the lines is (4,2)
• D. All of the above.

Answer 1

The correct option is D All of the above.

(i) From the figure, we can see that the line AC passes through the points (0,0) and (2,1).

$\Rightarrow$ If the equation of AC is 2y = x, then points (0,0) and (2,1) should be its solutions.

On substituting x = 0 and y = 0 in the equation 2y = x, we get LHS = RHS = 0.

On substituting x = 2 and y = 1 in the equation 2y = x, we get LHS = RHS = 2.

Therefore, it is verified that points (0,0) and (2,1) are solutions of equation 2y = x, and this equation represents the line AC.

(ii) From the figure, we can see that the line BD passes through (2,0) and (0,-2).

On substituting x = 2 and y = 0 in the equation y = x - 2, we get LHS = RHS = 0.

On substituting x = 0 and y = -2 in the equation y = x - 2, we get LHS = RHS = -2.

Therefore, it is verified that points (2,0) and (0,-2) are solutions of equation y = x - 2, and this equation represents the line BD.

(iii) From the graph we can see that both the lines intersect at point (4,2) .