B is the midpoint of AC and D is the midpoint of CE. Solve for BD given that BD = 2y + 8 and AE = 6y +12

Answer 1

Since B is the midpoint of AC, we can say that AB = BC.

Similarly, since D is the midpoint of CE, we can say that CD = DE.

Given that AE = 6y + 12, we can also say that AC = AE + EC.

Since B is the midpoint of AC, AB = BC, so AB = AC/2.

And since D is the midpoint of CE, CD = DE, so CD = EC/2.

Now let's try to find the values of AC and EC:

AC = AE + EC
AC = (6y + 12) + EC

Since B is the midpoint of AC, AB = AC/2
AB = (AE + EC)/2
AB = ((6y + 12) + EC)/2

We can now set up an equation using AB and BC:

AB = BC
((6y + 12) + EC)/2 = EC/2

Now we can solve for EC:

6y + 12 + EC = EC
6y + 12 = 0
6y = -12
y = -2

Substitute y = -2 into the given value of BD:

BD = 2y + 8
BD = 2(-2) + 8
BD = -4 + 8
BD = 4

Therefore, BD = 4.