Question

Please help me! Given triangle ABC with A(-4,-2), B(4,4), and C(18,-8) write the equation of the line containing the altitude that passes through point B in STANDARD FORM. SHOW WORK. NEED THE EQUATION PLS. Write the equation of the line containing the media. that passes through point C in SLOPE-INTERCEPT FORM.

Answer 1

ALTITUDE
the altitude is the height of the traignel

if we graph the points, we get some lopsided triangle
so we know the altitude is peerpendicular to the base
so find the line that is perpendicular to the line tha passes through A and C

so first fid the line that passes through (-4,-2) and (18,-8)
slope=(y2-y1)/(x2-x1)
slope=(-8-(-2))/(18-(-4))=(-8+2)/(18+4)=-6/22
perpendicular lines have slopes the multipy to -1
-6/22 times what=-1
times both sides by -22/6
wat=22/6
that is the slope of the line that is the altitude

we have to use point slope form
the equation of a line that passes through (x1,y1) and has sloe of m is
y-y1=m(x-x1)
so passes through B (4,4) and has slope of 22/6
y-4=22/6(x-4)
y-4=22/6x-44/3
y=(22/6)x-32/3
that is the altitude






MEDIAN
the media is the line joining the midpoint of one side to the vertex of the other
so we need to find the line that passes through the midpoint of AB and through the point C
midpoint of (x1,y1) and (x2,y2) is
((x1+x2)/2,(y1+y2)/2)
so
midopint of (-4,-2) and (4,4) is
((-4+4)/2,(-2+4)/2)=(0/2,2/2)=(0,1)

so we just find the line that passes through (0,1) and (18,-8)
slope iis (-8-1)/(18-0)=-9/18=-1/2
a point is (0,1) and sloe si -1/2
y-1=-1/2(x-0)
y-1=1/2x
y=(1/2)x+1








ALTITUDE
y=(-6/22)x

MEDIAN:
y=(1/2)x+1