What is the area of the smaller triangle (10,2)(12,2)(12,6) in relation to the area of the larger triangle (2,3)(5,3)(5,9)?
To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height
For the larger triangle, the base is the difference in x-coordinates of the two vertices on the same horizontal line, which is 5 - 2 = 3. The height is the difference in y-coordinates of the two vertices on the same vertical line, which is 9 - 3 = 6. Therefore, the area of the larger triangle is:
(1/2) * 3 * 6 = 9
Now, let's find the coordinates of the vertices of the smaller triangle.
The base of the smaller triangle is the difference in x-coordinates of the vertices on the same horizontal line, which is 12 - 10 = 2. The height is the difference in y-coordinates of the vertices on the same vertical line, which is 6 - 2 = 4. Therefore, the area of the smaller triangle is:
(1/2) * 2 * 4 = 4
In conclusion, the area of the smaller triangle is 4 and the area of the larger triangle is 9.