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Hi Can you please help my son with this problem?

Hi Can you please help my son with this problem?-example-1

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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.

User Thaddeus
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