Determine the x- and y-coordinates of the trapezoidal shape.

[Ella Tankersley]

Homework Statement

**I couldn't get my specific picture to copy but here is one that is the same except, 2.6b=1.7b and 2.0b = 1.3b**

Determine the x- and y-coordinates of the trapezoidal shape.
(X bar, Y bar) =

Homework Equations

X bar = ∫xdA / ∫dA
Y bar = ∫ydA/∫dA

The Attempt at a Solution

point 1: (b, 1.7b)
point 2: (1.3b,0)
m = -1.7/.3
x=-.3/1.7y+66.3/51

dA = (-.3y/1.7+66.3/51)dy
x=(-.3y/1.7+66.3/51)/2
y=y
X bar = ∫₀^1.7b((-.3y/1.7+66.3/51)/2)(-.3y/1.7+66.3/51)dy/ (∫₀^1.7b(-.3y/1.7+66.3/51)dy) = 2.07
Y bar = ∫₀^1.7b(y(-.3y/1.7+66.3/51)dy/ (∫₀^1.7b((-.3y/1.7+66.3/51)dy) = 0.9826

I'm not sure if there was a better way to write out my solution but let me know if you don't understand anything. Thank you!

 

[haruspex]

X bar = ... = 2.07

Putting it outside the figure?

 

[haruspex]

if there was a better way to write out my solution

LaTeX would best. Failing that, you can use subscripts and superscripts (X₂, X² in the bar above the text entry area) for bounds.