 | George Hale Puckle - Conic sections - 1887 - 404 pages
...length vf the perpendicular from the point (x = 3, y = u on the line (Sy-7* + 9=0). 3x5-7x3+9 3 Z = 53i. To find the area of a triangle in terms of the coordinates of the angular points, the axes being rectangular. Let the 'three points be (xy), (x'y), (x"y"). The equation... | |
 | John Daniel Runkle - Geometry, Analytic - 1888 - 370 pages
...these coordinates are proportional to .••' and y'. . k y'x"-x'y" * "'" I x'y'"-y'x'"' Areas. 7. To find the area of a triangle in terms of the coordinates of its vertices. o FIG. 6. First, when the axes are rectangular. Let A(x'y'), B(x"y"), C(x'"y'") be the vertices.... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...In an ellipse, if CD be a semi-diameter conjugate to CP, show that 8. Investigate an expression for the area of a triangle in terms of the coordinates of its three angular points. E, F, G, /if are points in the four sides of a square ABCD, such that AE=\AB,... | |
 | William Shaffer Hall - Measurement - 1893 - 88 pages
...AF= 8; what is the area of the entire figure? AREA OF POLYGONS BY THE METHOD OF COORDINATES. § 30. To find the area of a triangle in terms of the coordinates of its angular points. FIG. 10. Two intersecting straight lines are regarded as the lines of reference and are called axes.... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...the following steps : The del/ = 2 (- 25) + 5 (- 56) - 4 (- 163) = —50 — 280 + 652 = 3«. § 22. To find the area of a triangle in terms of the co-ordinates of its vertices. Y _ Let the vertices be AtayJ, B(x2y2), C(x3ys) Through А, В, С draw IIя to the axes.... | |
 | Edinburgh Mathematical Society - Mathematics - 1893 - 352 pages
...and on transformation to the other systems we readily obtain the above expressions. 4. To find tlie area of a triangle in terms of the co-ordinates of its angular points. (1) Independently of the corresponding expression in Cartesians. If A' denote the area, since twice... | |
 | W. J. Johnston - Geometry, Analytic - 1893 - 462 pages
...beginners justifies this innovation. The generality of the usual trapezium proof of the formula for the area of a triangle in terms of the co-ordinates of its vertices is invalid without a more detailed examination than is usual of the consequences of the convention... | |
 | Queen's University (Kingston, Ont.) - 1899 - 920 pages
...through a given point. Queen's University Ej-aminationt : Aprü, 1900. HONOURS. Conies, I. 1. Determine the area of a triangle in terms of the coordinates of its vertices. 2. (a) Obtain the standard equation of a line ; and explain the geometrical meaning of the... | |
 | University of Sydney - 1900 - 646 pages
...the perpendicular distance of the line from A. ANALYTICAL GEOMETRY. TWO HOURS. 1. Find a forrmila for the area of a triangle in terms of the coordinates of its angular points. Find the area of the triangle formed by the lines .c + 2y=0, j- — oy = 0 and x = S. 2. Shew that... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...4^ + 7 = 0 and 4^-3^+1 =o which make angles of 60° with the former line. 4. Find an expression for the area of a triangle in terms of the coordinates of its angular points. Find the area of the triangle whose sides are y - x, y = 2x, x +y -6 = 0. 5. Form the equation of a... | |
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Find an expression for the area of a triangle in terms of the coordinates of its angular points. 
