(b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Yɔ), · .. (X area of the polygon. O A 2 = (X1V2 + X2V1) + (x2V3 + X3Y2) + … + (x, – 1Yn + XnYn - 1) + (x,Y1 + x1 O A = (x2Y1 - X1Y2) + (x3Y2 - X2Y3) + · . + (x,Yn-1 - Xn-1Yn) + (x1Yn - X,Y1-
(b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Yɔ), · .. (X area of the polygon. O A 2 = (X1V2 + X2V1) + (x2V3 + X3Y2) + … + (x, – 1Yn + XnYn - 1) + (x,Y1 + x1 O A = (x2Y1 - X1Y2) + (x3Y2 - X2Y3) + · . + (x,Yn-1 - Xn-1Yn) + (x1Yn - X,Y1-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Needed to be solved b and c part's correctly in 30 minutes and get the thumbs up please show neat and clean work please
![(a) If C is the line segment connecting the point (x,, y1) to the point (x2, y2), find the following.
x dy – y dx
(b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), . .., (x,, Y,), find the
area of the polygon.
O A =
(X1Y2 + X2Y1) + (X2V3+ X3Y2) +
** + (x, – 1Yn + XnYn - 1) + (x,Y1 + X1Yn)
O A ==(x>Y1 - X,V2) + (x3V2 = X3Y3) + •…· + (x,Yn-1 - Xn-1Yn) + (x;Vn= XpY2)]
+...
O A =
(x,V2 - X2Y1) – (×2V3 - X3V2) – ·.. - (Xp - 1Yn – XpYn – 1) + (x,V1 – X1Vn}|
O A = (X1V2 - X2V1) + (x2V3 – X3Y2) + .. + (Xn – 1Vn – XpYn - 1) + (x,V1 – x1Vn)
O A = (x1Y2 - x2Y1) + (x2Y3 - X3V2) + · · + (Xn – 1Yn – XnYn – 1) + (xnY1 - X1YN)
(c) Find the area of the pentagon with vertices (0, 0), (3, 1), (1, 2), (0, 1), and (-2, 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bb3e301-f8e2-46e0-b9b7-f5f7c2b96785%2Fb3a19e0e-b7aa-4d48-b351-45862bbde5b5%2Fsf09al_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) If C is the line segment connecting the point (x,, y1) to the point (x2, y2), find the following.
x dy – y dx
(b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), . .., (x,, Y,), find the
area of the polygon.
O A =
(X1Y2 + X2Y1) + (X2V3+ X3Y2) +
** + (x, – 1Yn + XnYn - 1) + (x,Y1 + X1Yn)
O A ==(x>Y1 - X,V2) + (x3V2 = X3Y3) + •…· + (x,Yn-1 - Xn-1Yn) + (x;Vn= XpY2)]
+...
O A =
(x,V2 - X2Y1) – (×2V3 - X3V2) – ·.. - (Xp - 1Yn – XpYn – 1) + (x,V1 – X1Vn}|
O A = (X1V2 - X2V1) + (x2V3 – X3Y2) + .. + (Xn – 1Vn – XpYn - 1) + (x,V1 – x1Vn)
O A = (x1Y2 - x2Y1) + (x2Y3 - X3V2) + · · + (Xn – 1Yn – XnYn – 1) + (xnY1 - X1YN)
(c) Find the area of the pentagon with vertices (0, 0), (3, 1), (1, 2), (0, 1), and (-2, 1).
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