find the equation of the line that passes through (-2,1) and is perpendicular to the points A(-2,3) and B(4,-1)
To find the equation of the line, we first need to find the slope of the line that is perpendicular to the line passing through points A(-2,3) and B(4,-1).
The slope of the line passing through points A(-2,3) and B(4,-1) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we have:
m = (-1 - 3) / (4 - (-2))
m = (-4) / (6)
m = -2/3
Since the line we want to find is perpendicular to this line, the slope of our line will be the negative reciprocal of -2/3, which is 3/2.
Now we have the slope of the line that passes through (-2,1) and is perpendicular to the line passing through points A(-2,3) and B(4,-1).
Using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line, we can plug in the values:
(y - 1) = (3/2)(x - (-2))
Simplifying, we have:
y - 1 = (3/2)(x + 2)
Multiplying through by 2 to eliminate the fraction, we have:
2y - 2 = 3(x + 2)
Expanding, we have:
2y - 2 = 3x + 6
Bringing like terms to one side of the equation, we get:
3x - 2y = -8
So, the equation of the line that passes through (-2,1) and is perpendicular to the line passing through points A(-2,3) and B(4,-1) is 3x - 2y = -8.