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. (a) Let C be the line segment from a point (a, b) to a point (c, d). Show that -ydx + xdy = ad – be (b) Use the result in part (a) to show that the area A of a triangle with successive vertices (x1, yı), (x2, y2), and (X3, y3) going counterclockwise is A - (x1y2 – xzyı) + (x2y3 – x3y2) + (x3yı – xıy3)] (c) Find a formula for the area of a polygon with succes- sive vertices (x1, yı), (x2, y2), ...(Xn, Yn) going coun- terclockwise. (d) Use the result in part (c) to find the area of a quadrilat- eral with vertices (0, 0), (3, 4), (–2, 2), (–1,0).

. (a) Let C be the line segment from a point (a, b) to a point (c, d). Show that -ydx + xdy = ad – be (b) Use the result in part (a) to show that the area A of a triangle with successive vertices (x1, yı), (x2, y2), and (X3, y3) going counterclockwise is A - (x1y2 – xzyı) + (x2y3 – x3y2) + (x3yı – xıy3)] (c) Find a formula for the area of a polygon with succes- sive vertices (x1, yı), (x2, y2), ...(Xn, Yn) going coun- terclockwise. (d) Use the result in part (c) to find the area of a quadrilat- eral with vertices (0, 0), (3, 4), (–2, 2), (–1,0).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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. (a) Let C be the line segment from a point (a, b) to a point (c, d). Show that -ydx + xdy = ad – be (b) Use the result in part (a) to show that the area A of a triangle with successive vertices (x1, yı), (x2, y2), and (X3, y3) going counterclockwise is A - (x1y2 – xzyı) + (x2y3 – x3y2) + (x3yı – xıy3)] (c) Find a formula for the area of a polygon with succes- sive vertices (x1, yı), (x2, y2), ...(Xn, Yn) going coun- terclockwise. (d) Use the result in part (c) to find the area of a quadrilat- eral with vertices (0, 0), (3, 4), (–2, 2), (–1,0).
Transcribed Image Text:. (a) Let C be the line segment from a point (a, b) to a point (c, d). Show that -ydx + xdy = ad – be (b) Use the result in part (a) to show that the area A of a triangle with successive vertices (x1, yı), (x2, y2), and (X3, y3) going counterclockwise is A - (x1y2 – xzyı) + (x2y3 – x3y2) + (x3yı – xıy3)] (c) Find a formula for the area of a polygon with succes- sive vertices (x1, yı), (x2, y2), ...(Xn, Yn) going coun- terclockwise. (d) Use the result in part (c) to find the area of a quadrilat- eral with vertices (0, 0), (3, 4), (–2, 2), (–1,0).
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