How do you find the area of a triangle bounded by the y axis, the line f(x) = 7 - 4/5 x, and the line perpendicular to f(x) that passes through the origin?

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Answer 1 · 2018-08-02T12:54:44

Area of the triangle is #11.95# sq.unit

#f(x)=y= 7- 4/5 x# , slope is # m=-4/5#

Slope of perpendicular line is # m_p= -1/(-4/5)=5/4#

Equation of perpendicular line passing through origin is

#y=5/4 x# , intersecting point between the lines is

#5/4 x= 7- 4/5 x or 25 x= 140- 16 x or 41 x = 140#

#:. x = 140/41 , y= 5/4*140/41=175/41#

y intercept of line is #y= 7- 4/5 x ; y= 7# , so the triangle is

bounded by the points #(0,0) ,(0,7) and (140/41,175/41)#

Area of the triangle is #A_t=1/2*7*140/41=490/41~~ 11.95#

Area of the triangle is #11.95# sq.unit [Ans]