Question 1127239
Find the area of a triangle bounded by:
 the y-axis, 
the line {{{f(x) = 6 -(6/7)x}}}=> a slope={{{ (-6/7)}}}
the line perpendicular to f(x) that passes through the origin

first find perpendicular line {{{y=mx}}}

{{{m=-1/(-6/7)=7/6}}}

{{{y=(7/6)x}}}




find intersection point both lines:

{{{(7/6)x) = 6 -(6/7)x}}}

{{{(7/6)x+(6/7)x = 6 }}}

{{{(7/6+6/7)x = 6 }}}

{{{(85/42)x = 6 }}}

{{{x = 6/(85/42) }}}

{{{x = 2.96 }}}

find {{{y}}}

{{{y=(7/6)2.96}}}

{{{y=3.45}}}

intersection point {{{C}}} is at ({{{2.96}}},{{{3.45}}})


graph all:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2.96,3.45,.12),locate(3,3.45,highlight(C(2.96,3.45))),
locate(0.2,-0.2,highlight(A)),locate(0.2,6.3,highlight(B)),
 graph( 600, 600, -10, 10, -10, 10, 6 -(6/7)x, (7/6)x)) }}}


the length of the base: {{{AB=6}}}
the length of the altitude to the base: {{{2.96}}}

the area of the triangle {{{ABC}}} is:

{{{A=(1/2)*6*2.96}}}

{{{A=3*2.96}}}

{{{A=8.88}}} square units