•color(white)(x)[1/2(x_1+x_2),1/2(y_1+y_2)]∙x[12(x1+x2),12(y1+y2)]
"midpoint "=[1/2(-1+7),1/2(-3+1)]midpoint =[12(−1+7),12(−3+1)]
color(white)("midpoint ")=[1/2(6),1/2(-2)]=(3,-1)midpoint =[12(6),12(−2)]=(3,−1)
"calculate slope m using the "color(blue)"gradient formula"calculate slope m using the gradient formula
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)∙xm=y2−y1x2−x1
"let "(x_1,y_1)=-1,-3)" and "(x_2,y_2)=(7,1)let (x1,y1)=−1,−3) and (x2,y2)=(7,1)
rArrm=(1-(-3))/(7-(-1))=4/8=1/2⇒m=1−(−3)7−(−1)=48=12
"given a line with slope m then the slope of a line"given a line with slope m then the slope of a line
"perpendicular to it is"perpendicular to it is
•color(white)(x)m_(color(red)"perpendicular")=-1/m∙xmperpendicular=−1m
rArrm_"perpendicular"=-1/(1/2)=-2⇒mperpendicular=−112=−2
"the equation of a line in "color(blue)"point-slope form"the equation of a line in point-slope form is.
•color(white)(x)y-y_1=m(x-x_1)∙xy−y1=m(x−x1)
"where m is the slope and "(x_1,y_1)" a point on the line"where m is the slope and (x1,y1) a point on the line
"using "m=-2" and "(x_1,y_1)=(-1,-3)" then"using m=−2 and (x1,y1)=(−1,−3) then
rArry+1=-2(x-3)larrcolor(red)"in point-slope form"⇒y+1=−2(x−3)←in point-slope form
rArry+1=-2x+6⇒y+1=−2x+6
rArry=-2x+5larrcolor(red)"in slope-intercept form"⇒y=−2x+5←in slope-intercept form