 | University College, Galway - 1903 - 440 pages
...of AB, BC, CD, DA lie on a circle, then AC, BD are perpendicular. 5. "Write down the expression for the area of a triangle in terms of the coordinates of its angular points. Prove that the area of the triangle formed by the lines x = a, y = b, z/b + y/a = 1 is i (a2 - ab +... | |
 | Albert Luther Candy - Geometry, Analytic - 1904 - 288 pages
...internally in the ratio 8 : 4, and externally in the ratio 2 : 9. AREAS [10 AREAS OF POLYGONS 10.* To find the area of a triangle in terms of the coordinates of its vertices, the axes being inclined at an angle <a. CASE I. When one vertex is at the origin. Qj Q. Let... | |
 | Preston Albert Lambert - Algebra - 1907 - 110 pages
...a^ = x3 — xv -Z)3-D2 = xi P3 = (zs - xj (yl + + O2 - zs) O = xi ~ xv 33 This expression for double the area of a triangle in terms of the coordinates of its vertices is readily reproduced by arranging the coordinates of the vertices in order in two vertical... | |
 | Royal Military Academy, Woolwich - Mathematics - 1909 - 456 pages
...7 = o and 4x - 3^+ I = 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... | |
 | Henry Burchard Fine, Henry Dallas Thompson - Geometry, Analytic - 1909 - 336 pages
...left of the line x + a=0. Similarly for equations of the form У + Ъ = 0. 52. Problem. To express the area of a triangle in terms of the coordinates of its vertices, the axes being rectangular. The area of the triangle PiP2.P3 is one half the product of a... | |
 | Henry Burchard Fine, Henry Dallas Thompson - Geometry, Analytic - 1909 - 344 pages
...left of the line x + a=0. Similarly for equations of the form y + b = 0. D 52. Problem. To express the area of a triangle in terms of the coordinates of its vertices, the axes being rectangular. The area of the triangle P]P2P3 is one half the product of a... | |
 | American Mathematical Society - Mathematics - 1911 - 698 pages
...Determinants. More than half of it is devoted to applications in the domain of elementary analytic geometry : The area of a triangle in terms of the coordinates of its vertices and in terms of the equations of its sides ; the product of the areas of two triangles in... | |
 | Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...— 1y + 7 = 0 and 1x — 3y — 3 = 0 which make an angle of 45° with the line y — 2x. 2. Express the area of a triangle in terms of the coordinates of its vertices. Show that the ai-ea of the triangle formed by the lines ax2 4- 2bxy 4- cf1 = 0, y = mx 4-... | |
 | Charles Smith - Conic sections - 1916 - 466 pages
...divides the join of (2, 1) and (3, 5) externally in the ratio 2 : - 3. Ans. (0, - 7). 6. To express the area of a triangle in terms of the co-ordinates of its angular points. Let the co-ordinates of the angular points A, B, C be xi, yi! <*, yi; and x3, y, respectively. Draw... | |
 | University of Calcutta - 1916 - 802 pages
...sin (a + fl) + sin (a + 2a) — ... ; (2) sec «sec 29+ sec 2йаес 3e + sec 3« sec 4в+ ... 7. Find the area of a triangle in terms of the coordinates of its vertices, the axes being rectangular. The coordinates of А, В, С are (6, 3), ( — 3, 5), (4, —2)... | |
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Find an expression for the area of a triangle in terms of the coordinates of its angular points. 
