What is the slope of any line perpendicular to the line passing through #(-21,2)# and #(-32,5)#?

Question

Eva Abramson · Accepted Answer

slope of the perpendicular line #=11/3# First we need to find the slope of the line passing through the points: #(-21, 2) and (-32, 5)#, the slope #m# between the points: #(x_1, y_1) and (x_2, y_2)# is given by: #m=(y_2-y_1)/(x_2-x_1)#, so in this case: #m=(5-2)/(-32-(-21))#, simplifying we get: #m=3/(-32+21)=3/-11=-3/11# Now the perpendicular lines have slopes that are negative reciprocals, so if #m_1 and m_2# are the slopes of the two perpendicular lines then: #m_2=-1/m_1#, therefore in this case: #m_2= -1/(-3/11) = 11/3#

Genesis Allen · Answer

undefined To find the slope of the line passing through (-21,2) and (-32,5), we use the formula for slope: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $. Substituting the coordinates into the formula, we get $ m = \frac{{5 - 2}}{{-32 - (-21)}} = \frac{3}{-11} $. The slope of this line is $ -\frac{3}{11} $.

Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of any line perpendicular to the given line will be the negative reciprocal of $ -\frac{3}{11} $, which is $ \frac{11}{3} $. Therefore, the slope of any line perpendicular to the line passing through (-21,2) and (-32,5) is $ \frac{11}{3} $.