My first task was to find the coordinates of points A, B and C:
A - (1,0)
B - (7,0)
C - (1,7)
I then had to find the distance between each of the points, applying the distance formula:
√((y2 - y1)^2 - (x2 - x1))
Using this formula, I calculated:
AB = 7 units
AC = 6 units
To find the area of that triangle, I would use the formula:
1/2 x base x height
= 1/2 x 6 x 7
= 1/2 x 42
= 21 units
Now we know that the area of the bigger triangle is 21 units. To find the area of the shaded triangle, we must calculate the base and the height. To do this, we must find the coordinates of each point on the line, and find the distance applying the distance formula. Once this is done, we can find the area.
Base = 2 units
Height = 3 units
Area = 1/2 x 2 x 3
Area = 3 units
Therefore, the area of the shaded triangle one-seventh that of the original triangle.