Line A: y = 1 2 x + 2 Line B: y = − 1 2 x + 7 Line C: y = −2x + 4 Line D: y = 1 2 x + 5 4 Which lines are perpendicular? A) A and B B) A and C C) B and C D) A and D

Check the explanation.

Step-by-step explanation:

The slope-intercept form of the equation is

Line A:

The slope of line A:

    ∵ comparing with

Line B:

   ∵ comparing with

Line C:

    ∵ comparing with

Line D:

    ∵ comparing with

As we know that the product of the slopes of perpendicular lines is -1.

i.e. their slopes are opposite of the reciprocal of each other.

Now, let us check the OPTIONS:

Option A)  A and B

Check:

As the product of the slopes A and B is NOT -1, so the lines A and B are not perpendicular. Hence, option A is NOT true.

Option B)  A and C

As the product of the slopes A and C is NOT -1, so the lines A and C are not perpendicular. Hence, option B is NOT true.

Option C)  B and C

As the product of the slopes B and C is NOT -1, so the lines B and C are not perpendicular. Hence, option C is NOT true.

Option D)  A and D

As the product of the slopes A and D is NOT -1, so the lines A and D are not perpendicular. Hence, option D is NOT true.

Therefore, NO OPTION is correct.