What is the equation of the line that is perpendicular to the line passing through #(-5,3)# and #(-2,9)# at midpoint of the two points?

1 Answer
Feb 2, 2018

Answer:

#y=-1/2x+17/4#

Explanation:

#"we require to find the slope m and the midpoint of the"#
#"line passing through the given coordinate points"#

#"to find m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-5,3)" and "(x_2,y_2)=(-2,9)#

#rArrm=(9-3)/(-2-(-5))=6/3=2#

#"the slope of a line perpendicular to this is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m=-1/2#

#"the midpoint is the average of the coordinate of the"#
#"given points"#

#rArrM=[1/2(-5-2),1/2(3+9)]=(-7/2,6)#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#rArry=-1/2x+blarrcolor(blue)"is partial equation"#

#"to find b substitute the coordinates of the midpoint"#
#"into the partial equation"#

#6=7/4+brArrb=17/4#

#rArry=-1/2x+17/4larrcolor(red)"perpendicular line"#