Question

If line A contains the points (3, -4) and (6, -2), and line B contains the points (-1, 5) and (1, 2), prove that the lines are perpendicular by multiplying their slopes.

Answer 1

Answer:

Correct answer:  sa · sb = 2/3 · (- 3/2) = - 1

Step-by-step explanation:

Given:

line A - (x₁, y₁) = (3, -4)   and (x₂, y₂) = (6, -2)

line B - (x₁, y₁) = (-1, 5)   and (x₂, y₂) = (1, 2)

The slope is calculated using the following formula:

s = (y₂ - y₁) / (x₂ - x₁)

sa = (-2 - (-4)) / (6 - 3) = (-2 + 4) / 3 = 2 / 3

sa = 2 / 3

sb = (2 - 5) / (1 - (-1)) = -3 / 2

when lines are perpendicular to each other then the slopes are in the next relationship:

sa · sb = - 1

we will check:

sa · sb = 2/3 · (- 3/2) = - 1

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