...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 of A, X},y3, .........................

...of the 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),...

...co-ordinates of the point which divides a given line into two parts in the ratio of m to n. Ex. 153. Express the area of a triangle in terms of the co-ordinates of its angular points. Ex.154. Determine the co-ordinates of the point of intersection of the lines y=— x-\-l and y=x+2',...

...the geometrical interpretation of the similarity of the first of this equation to the expression for the area of a triangle in terms of the co-ordinates of its angular pointa. 4. Find the equation to the normal at any point of a 1O circle and show that it must pass through...

...ALLMAN, LL.D. 1. Prove that the area of any zone of a given sphere is in proportion to its height. 2. Find the area of a triangle in terms of the co-ordinates of its vertices, the axes being rectangular. Find the area of the triangle, the equations of whose sides are...

...inclined planes, when its centre of gravity divides it in the ratio m to ». 1 6. Prove the expression for the area of a triangle in terms of the coordinates of its vertices, and deduce the corresponding expression for a polygon. 17. Determine the angle between the...

...the straight line is to be bisected, then m—n, and we have 3. To find an analytical expression for the area of a triangle in terms of the co-ordinates of its angular points. Area =%\xty1 -x1y^ + x^y, -xty, + x1y,-xiy1 \. To remember this formula, observe that a; is in the...

...points may lie in a straight line, and interpret the resnlt geometrically. 3. Ohtain an expression for the area of a triangle in terms of the co-ordinates of its angnlar points. Find the area of the triangle inclnded hy the straight lines— x cos a, + y sin ai...

...(x, y) be equidistant from the two points (3, 4} and (1, - 2) , then will x + 3y = 5. * 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, G be xi> Vi> x*> &; and «vy, respectively. o K M...

...4035 л/(.г-лО*+ (y~yj+ 2 (xx) (yy) cos ». PBOOF.— By (Fig. 7), Eue. I. 47, and (702). Area A of a triangle in terms of the coordinates of its angular points a^y^ ж2у2> ж»Уз4036 A = i {дчу>— J»yi + .F, i/s— ^Sy2 + ¿од— ¿од} . PROOF. —...