...of graphic algebra. As minor criticisms, it is at once noticed that tho the proof of the formula for the area of a triangle in terms of the coordinates of its vertices is very neatly shown on page 15, its very simple and important extension to the areas of polygons,...

...Cv i - ya) + *3 (yi / the vertices of the triangle may be read in any order. The formula expressing the area of a triangle in terms of the coordinates of its vertices may be applied to find the area of any polygon. Equations and Graphs of Straight Lines y =...

...equations will be useful for the derivation of Section 2.7. First, we shall find an expression for the area of a triangle in terms of the coordinates of its vertices. Consider a triangle lying in the xy plane with one vertex at the origin (Figure 2.10a).The...

...the algebra can become very cumbersome. A useful result is the Coordinates-Area Formula, which gives the area of a triangle in terms of the coordinates of its vertices. If these coordinates are (xi,yi), (*2,2/2) and (X3,2/3), then the area of the triangle is...

...2/i 1 sinw d and on transformation to the other systems we readily obtain the above expressions. 4. To find the 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...

...oi+T^+ ...... is convergent if x is >1, divergent if x is = or <1. IV. CO-ORDINATE GEOMETRY. 1. Express the area of a triangle in terms of the co-ordinates of its angular points. The polar co-ordinates of three points are \3, ^J, (3, -^j, and ~ 3> 5 ) j find the rectangular co-ordinates...

...of indeterminate coefficients to find the sum of the series 1.2 + 2-3 + 3-4 + ...... + n (n+1). 7. Find the area of a triangle in terms of the co-ordinates of its angular points, and explain what the resulting sign indicates. Show that the area of the triangle contained by the...

...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 oar author straightway...

...: 4. Ex. 2. Show that the medians of a triangle are concurrent. 2.3. Area of a triangle. To express the area of a triangle in terms of the coordinates of its vertices. Let ABC be the triangle. Let the coordinates of A, B and C be i. yj, (*2. ;>*) and (x*, y*),...

...y= ±3-2, and make a rough drawing of the ellipse and the related lines. 8. Find an expression for the area of a triangle in terms of the co-ordinates of its vertices. If the vertices of a quadrilateral ABCD are at (10, 10), (1, 8), (3, 2), and (9, 5) respectively,...