...vector, its use illustrated by a few simple problems such as the division of a line in given ratio, the area of a triangle in terms of the coordinates of its vertices, and the location of the center of gravity of a system of weights. But our author straightway...

...B ). Show that the area of the polygon is EXAMINATION PAPER II. 1. Investigate a method of finding the area of a triangle in terms of the coordinates of its vertices. 2. Find the area of the triangle, the coordinates of whose angular points are (2,1), (3,...

...lying on four given lines, and one side passing through a given point. 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...

.../=(.*•-«)(>— 2fl)(j--3«) round the axis of .r. 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 the...

...and prove the property of the curve upon which the process is founded. 6. (a) Find an expression for the area of a triangle in terms of the coordinates of its vertices. (6) ABCD arc four points of which no three are in line. Prove that the area of the triangle...

...P^P^ = (* 3 - a^) (y x + y s ) Multiplying out and simplifying, 2 Area PPP 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 x \y\ in order in two vertical...

...x2y s + x s y ^ - y^ - y 2 x 3 the same result as was found for Case I. This expression for double the area of a triangle in terms of the coordinates of its vertices is entirely general. PROBLEM 50. Find the area of the triangle whose vertices are the points...

...left of the line x + a= 0. Similarly for equations of the form у -f. 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 Р^Р 3 is one half the product of a...

...right or left of the line x -f- a = 0. Similarly for equations of the form 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 PpP 2 P 3 is one half the product of...

...of the line x + a • = 0. Similarly for equations of the form. У + b = 0. 52. Problem. To express the area of a triangle in terms of the coordinates of its vertices, the axes beiutj reclanyulur. . The area of the triangle P t P 3 P 3 is one half the product...