Question

Line l has a slope of 2/3 The line through which of the following pair of points is perpendicular to l?

Answer 1

We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

The line through which of the following pair of points is perpendicular to l?

Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.

So, if line l has the slope 2/3.

Then the perpendicular lines have a slope equal to -3/2.

Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.

If we define (x₁, y₁) = (0, 0), then the other point must be:

$a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2$

Then we can write the other point as (2, -3).

So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

If you want to learn more about linear equations:

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