Find the slope of a line perpendicular to the line passing through the given points P(6,-1),Q(3,-2).
-3?
correct
Thanks
To find the slope of a line perpendicular to another line, you can use the relationship that the slopes of perpendicular lines are negative reciprocals of each other.
First, let's find the slope of the line passing through the points P(6, -1) and Q(3, -2). The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates of the points P and Q, we can calculate the slope of the line passing through them:
slope = (-2 - (-1)) / (3 - 6)
= (-2 + 1) / (3 - 6)
= -1 / (-3)
= 1/3
So, the slope of the line passing through P and Q is 1/3.
Now, to find the slope of the line perpendicular to this line, we take the negative reciprocal of 1/3. The negative reciprocal can be found by flipping the fraction and changing the sign:
Slope of line perpendicular = - 1 / (1/3)
= -1 * (3/1)
= -3
Therefore, the slope of the line perpendicular to the line passing through the points P(6, -1) and Q(3, -2) is -3.