(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,, Y1), (x2, Y2), ..., (Xp Yn), find the area of the polygon.O A = (x2V1 - X1¥2) + (×3V2 - X2V 3) + ·…· + (x,Yn-1 - xn-1Yn) + (×1Yn - x2O A =+ x2y1) + (x2y3 + x3¥2) + ·.. + (x, – 1ýn + X„Yn – 1) + (x,Y1 + x1Vn)1O A =(x,Y2 - X2Y2) + (xzY3 = X3Y2) + ·· + (x, - 1'n – x„Yn - 1) + (x,V1 - X4Yn}]1O A = (x,y2 - ×2Y1) - (X2Y3 - X3Y2) –. - (x, - 1Yn – xnYn - 1) + (x„Y1 - X1Vn]O A = (x,y2 - X2Y1) + (x2Y3 - X3V2) + .. + (x, - 1n - x,Yn - 1) + (x,Y1 - ×1¥n)(c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).

Answered: Image /qna-images/answer/f2023f8e-eeab-44f1-8197-0a10208e5952.jpg

(a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the following. x dy – y dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), ..., (xp Y), find the area of the polygon. O A (x2Y1 - ×1¥2) + (X3V2 - X2Y3) + ·…· + (X,Yn-1 – Xn-1Vn) + (×1V, – X„Y1) ... 4 = =(xxv2 + x2Y1) + (x2Y3 + X3Y2) + •·· + (x, - 1Yn + XnYn - 1) + (x„V1 + ×q¥n}] (xqY2 - x2yq) + (xzy3 - X3Y2) + •·· + (x, - 1Yn - x,Yn - 1) + (x,V1 – x;Yn +...+ O A = (x,V2 - x2Y;) – (X2Y3 - X3V2) – - (xp – 1Yn – x,Yn - 1) + (x„V1 - xqY½)| O A = (X1Y2 - X2Y1) + (×2Y3 - X3V2) + … + (x, - 1Yn – X„Yn – 1) + (x„Y1 - ×1V) ... (c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).

(a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the following. x dy – y dx (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Y2), ..., (xp Y), find the area of the polygon. O A (x2Y1 - ×1¥2) + (X3V2 - X2Y3) + ·…· + (X,Yn-1 – Xn-1Vn) + (×1V, – X„Y1) ... 4 = =(xxv2 + x2Y1) + (x2Y3 + X3Y2) + •·· + (x, - 1Yn + XnYn - 1) + (x„V1 + ×q¥n}] (xqY2 - x2yq) + (xzy3 - X3Y2) + •·· + (x, - 1Yn - x,Yn - 1) + (x,V1 – x;Yn +...+ O A = (x,V2 - x2Y;) – (X2Y3 - X3V2) – - (xp – 1Yn – x,Yn - 1) + (x„V1 - xqY½)| O A = (X1Y2 - X2Y1) + (×2Y3 - X3V2) + … + (x, - 1Yn – X„Yn – 1) + (x„Y1 - ×1V) ... (c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 1), and (-1, 1).

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.1: The Coordinate Plane

Problem 34E: In these exercises we find the area of plane figures. Plot the points P(5,1),Q(0,6) and R(5,1) on a...

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