What is the ratio of the area of the smaller triangle in relation to the area of the large triangle
Large triangle= (2, 3), (5, 9),and (5, 3)
Small triangle = (10, 2), (12, 6), and )12, 2)
To find the ratio of the area of the smaller triangle to the area of the large triangle, we need to calculate the areas of both triangles.
Using the coordinates of the large triangle: (2, 3), (5, 9), and (5, 3)
We can find the base and height of the large triangle:
Base = |5 - 2| = 3
Height = |9 - 3| = 6
Area of the large triangle = (1/2) * base * height = (1/2) * 3 * 6 = 9 square units
Similarly, using the coordinates of the small triangle: (10, 2), (12, 6), and (12, 2)
We can find the base and height of the small triangle:
Base = |12 - 10| = 2
Height = |6 - 2| = 4
Area of the small triangle = (1/2) * base * height = (1/2) * 2 * 4 = 4 square units
Therefore, the ratio of the area of the smaller triangle to the area of the large triangle is:
4/9 or 4:9