 | 1845 - 356 pages
...quadrilateral, PB the positive axis of x, and the points A, B, C, D, respectively, Now the expression for the area of a triangle in terms of the co-ordinates of its three angular points (#1^1, x^y- a .r 3 ^ 3 ) in reference to rectangular axes is ( Young's Analytical... | |
 | George Biddell Airy - Trigonometry - 1855 - 121 pages
...when one angle is found, the theorem of (64) may be applied. (67.) From the last expression we derive the formula for the area of a triangle in terms of the sides. For CA.BD a&sinC , — __ __ the area = — = — - = Vs . (s — a) . (s — b) , (s — c).... | |
 | Isaac Todhunter - Calculus of variations - 1861 - 578 pages
...Wy rfy/r [74. There are two methods of arriving at this result ; we may take the ordinary expression for the area of a triangle in terms of the co-ordinates of its angular points, and substitute the values of the co-ordinates just given. Or we may proceed thus... | |
 | Mathematics - 1862 - 428 pages
...2A then 2 A = It , dbc 1=(2A? ft flS* therefore 2A' and «' = - 2 /37 |« - 22 which are expressions for the area of a triangle in terms of the coordinates of its angular poiuts ; and for the length of a line in terms of the coordinates of its extremities. II.—... | |
 | Benjamin Theophilus Moore - Measurement - 1863 - 320 pages
...the figure of Art. 17. Here and, by the formula, =4(#2 +J/2), as before. 19. To find an expression for the area of a triangle in terms of the coordinates of its angular points. Let ABC be any triangle, OX, OY axes of coordinates. Let xI, y,, be the coordinates... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...1 +- 2 fo - aj (y a - yj COS ft). And any other case may be treated in like manner. 11. To express the area of a triangle in terms of the coordinates of the angular points, 2 , x 3 y B respectively, the axes being inclined at an angle CD. Y Draw the ordinates... | |
 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...y,)* + 2 (a;* - xj (y, - y.) cos w. And any other case may be treated in like manner. 11. To express the area of a triangle in terms of the coordinates of the angular points. xty, respectively, the axes being inclined at an angle w. Q LMNX Draw the ordinates... | |
 | George Hale Puckle - Conic sections - 1868 - 388 pages
...perpendicular from the point (x = S, y=5) on the line (Sy- 7a; + 9 = 0). .3x5-7x3+9 3 53 *. To find the area of a triangle in terms of the coordinates of the angular points, the axes being rectangular. Let -the co-ordinates of the three points be (xy), (x'y'),... | |
 | COUNCIL ON EDUCATION, SOUTH KENSINGTON - 1869 - 986 pages
...isosceles triangles. 4. Co-ordinate Geometry and Conic Sections.—Co-ordinates of a point. To express the area of a triangle in terms of the co-ordinates of the angular points. Locus of an equation. Equation to a curve. Equation to a straight line in various forms... | |
 | Dublin city, univ - 1871 - 366 pages
...and the internal segment from the perpendicular to the acute angle. (a). Deduce from this proposition the formula for the area of a triangle in terms of the sides. (6). If the sides are 0.23, 0.34, 0.45, find the area. 9. If from a point two right lines be... | |
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Applying the formula for the area of a triangle in terms of the coordinates of its vertices, we get Area of AABC = \ (2(0 -2) + 3(2 -3) + (-4) (3-0)} =- 19/2. 
