Question

Find the equation of the line that passes through (-2,1) and is perpendicular to the line AB

Answer 1

Find the equation of the line that passes through (-2,1) and is perpendicular to the line A(-2,3) and B(4,-1)

Answer 2

Since we don't know the equation of the line AB, we cannot determine the equation of the line perpendicular to it passing through (-2,1).

Answer 3

First, let's find the slope of the line AB. The formula for the slope between two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

Using the points A(-2,3) and B(4,-1), we can calculate the slope of the line AB:

m_AB = (-1 - 3) / (4 - (-2)) = -4 / 6 = -2 / 3

The line perpendicular to AB will have a slope that is the negative reciprocal of -2/3. The negative reciprocal of a fraction a / b is -b / a.

Thus, the slope of the line perpendicular to AB is:

m_perpendicular = -1 / (-2 / 3) = 3 / 2

Now, we have the slope of the line perpendicular to AB and a point on that line (-2, 1). We can use the point-slope form of a linear equation:

y - y1 = m (x - x1)

Substituting (-2, 1) for (x1, y1) and 3/2 for m, we get:

y - 1 = (3/2)(x - (-2))

Simplifying the equation:

y - 1 = (3/2)(x + 2)

Expanding:

y - 1 = (3/2)x + 3

Rearranging to slope-intercept form:

y = (3/2)x + 4

Therefore, the equation of the line that passes through (-2,1) and is perpendicular to the line AB is y = (3/2)x + 4.