...(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)...

...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....

...the line ax + by + c = Q the following simple method, which requires only a knowledge of the formula for the area of a triangle in terms of the coordinates of the vertices, may be employed. Y t Ci'O) (i) The given straight line cuts the ж-axis in the point...

...form 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,...

...triangles. The 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...

...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 =...

...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...

...lines z= ±1-9, 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,...

...EXAMPLE 5 Find the area of the triangle formed by A(2, 3), B(3, 0) and C(-4,2). 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. Note that we get area of...

...: 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*),...