B is the midpoint of Symbol for segment A C. .
AB=5x+2
AC=12x-2
What is the value of BC? Show your work for credit.
Line segment A C with point B on it.
Did you make a sketch?
On my diagram
length(BC) = length(AC) - length(AB)
= 12x-2 - (5x+2)
= 7x-4
but B is the mipoint, so AB = BC
7x-4 = 5x+2
2x = 6
x = 3
then BC = 7(3)-4 = 17
check:
AB = 17
AC = 12(3)-2 = 34
BC = 17 , YUP!!
B is the midpoint of segment AC and C is the midpoint of segment AE. If BC = 12 what is BE?
To find the value of BC, we first need to understand the properties of a midpoint. A midpoint is a point that divides a line segment into two equal parts. In this case, point B is the midpoint of segment AC.
To find the value of BC, we can use the fact that the lengths of the two parts of the segment are equal. In other words, the length of AB is equal to the length of BC.
Given:
AB = 5x + 2
AC = 12x - 2
We can set up an equation, equating AB and BC, and solve for x:
AB = BC
5x + 2 = BC
Now, we need to find the value of x. To do this, we can equate the lengths of AB and AC:
AB = AC
5x + 2 = 12x - 2
By rearranging the equation and simplifying, we have:
5x - 12x = -2 - 2
-7x = -4
Next, we can solve for x by dividing both sides of the equation by -7:
x = (-4) / (-7)
x = 4/7
Now that we have the value of x, we can substitute it back into the equation for BC:
BC = 5x + 2
BC = 5(4/7) + 2
BC = 20/7 + 2
BC = 20/7 + 14/7
BC = 34/7
Therefore, the value of BC is 34/7.