#"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"#
