Answer:
A= -2/5
Explanation:
To find the value of 'a' in this problem, you can use the midpoint formula, which states that the midpoint of two points (D and E in this case) is the average of their coordinates. In this case, you're given that the midpoint M is (3a, -6), and the coordinates of D and E are (a, -1) and (-2, -11), respectively.
The midpoint formula is:
M(x, y) = [(Dx + Ex) / 2, (Dy + Ey) / 2]
Using the coordinates of D and E:
M(x, y) = [(a - 2) / 2, (-1 - 11) / 2]
Now, you know that M(x, y) is (3a, -6), so you can set up the equations as follows:
3a = (a - 2) / 2
-6 = (-1 - 11) / 2
Let's solve these equations one by one:
Solve the first equation for 3a:
3a = (a - 2) / 2
Now, cross-multiply to get rid of the fraction:
6a = a - 2
Now, isolate 'a' by moving 'a' to one side and the constant to the other side:
6a - a = -2
5a = -2
Now, divide both sides by 5 to solve for 'a':
a = -2 / 5
The second equation is already simplified:
-6 = (-1 - 11) / 2
Now, calculate the right side:
-6 = (-12) / 2
-6 = -6
Both equations are satisfied, and you've found that a = -2/5.