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If a linear equation has solutions $(- 2, 2) (0, 0)$ and $(2, - 2),$ then it is of the form

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y - x = 0

x + y = 0

- 2 x + y = 0

- x + 2 y = 0

answer is B.

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Detailed Solution

Given that, the solutions of a linear equation are

(- 2, 2) (0, 0)

and

(2, - 2)

.
The equation of the form

ax + by + c = 0

for which the coordinate (x,y) satisfies the equation is the solution of the equation.
Consider the standard form of linear equation in two variables,

x + by + c = 0

.
Since the points

(- 2, 2), (0, 0)

and

(2, - 2)

are solutions to the linear equations, it satisfies the equation.
For the point

(- 2, 2)

a (- 2) + b (2) + c = 0

\Rightarrow - 2 a + 2 b + c = 0 \dots \dots \dots (1)

For the point

(0, 0)

\Rightarrow a (0) + b (0) + c = 0

\Rightarrow c = 0 \dots \dots \dots (2)

For the point

(2, - 2)

a (2) + b (- 2) + c = 0

\Rightarrow 2 a - 2 b + c = 0 \dots \dots \dots (3)

Substitute

c = 0

in equation (1),

\Rightarrow - 2 a + 2 b + 0 = 0

\Rightarrow - 2 a + 2 b = 0

\Rightarrow 2 a = 2 b

\Rightarrow a = b

Substitute

a = a, b = a

and

c = 0

ax + by + c = 0

to obtain the required equation.

\Rightarrow ax + ay + 0 = 0

\Rightarrow a (x + y) = 0

\Rightarrow x + y = 0

Therefore, if a linear equation has solutions

(- 2, 2), (0, 0)

and

(2, - 2)

then it is of the form

x + y = 0

.
Therefore, option (2) is correct.

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