If C is the line segment connecting the point (x1, Yı) to the point (x2, Y2), find the following. x dy - y dx

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 37E: Given: AB is an external tangent to O and Q at points A and B; radii lengths for O and Q are 4 and...
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(a) If C is the line segment connecting the point (x1, Yı) to the point (x2, Y2), find the following.
х dy — у dx
(b) If the vertices of a polygon, in counterclockwise order, are (x1, Yı), (x2, Y2), ..., (Xp, Yn), find the area of the polygon.
O A = (x1y2 - x2Y1) + (x2y3 – X3Y2) + ·.. + (X, - 1Yn – XnYn - 1) + (XnY1 – Xx1Vn)
O A = (X1V2 - X2Y1) + (X2y3 - X3Y2) + . + (Xn - 1Yn - XnYn – 1) + (xpY1 - X1Vn)
O A =(x2y1 – ×1V2) + (x3V2 - x2Y3) +
+ (XnYn-1 – Xn-1Yn) + (x1yn – XnY1)
...
2
O A =
(x1Y2 - X2Y1) – (X2y3 – ×3V2) – ... - (Xn - 1Yn - XnYn – 1) + (Xny1 – X1Yn)|
O A =
(x1Y2 + X2y1) + (x2y3 + X3y2) + ...
+ (Xn - 1Yn + Xnyn – 1) + (XnY1 + X1Yn)
(c) Find the area of the pentagon with vertices (0, 0), (5, 1), (1, 2), (0, 1), and (-2, 1).
Transcribed Image Text:(a) If C is the line segment connecting the point (x1, Yı) to the point (x2, Y2), find the following. х dy — у dx (b) If the vertices of a polygon, in counterclockwise order, are (x1, Yı), (x2, Y2), ..., (Xp, Yn), find the area of the polygon. O A = (x1y2 - x2Y1) + (x2y3 – X3Y2) + ·.. + (X, - 1Yn – XnYn - 1) + (XnY1 – Xx1Vn) O A = (X1V2 - X2Y1) + (X2y3 - X3Y2) + . + (Xn - 1Yn - XnYn – 1) + (xpY1 - X1Vn) O A =(x2y1 – ×1V2) + (x3V2 - x2Y3) + + (XnYn-1 – Xn-1Yn) + (x1yn – XnY1) ... 2 O A = (x1Y2 - X2Y1) – (X2y3 – ×3V2) – ... - (Xn - 1Yn - XnYn – 1) + (Xny1 – X1Yn)| O A = (x1Y2 + X2y1) + (x2y3 + X3y2) + ... + (Xn - 1Yn + Xnyn – 1) + (XnY1 + X1Yn) (c) Find the area of the pentagon with vertices (0, 0), (5, 1), (1, 2), (0, 1), and (-2, 1).
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