B is the midpoint of segment AC. AB = 5x and BC = 3x + 4. Find AB, BC and AC.
5x = 3x +4
-3x -3x
2x= 4
/2 /2
x =2
so Ab is 5 *2 which is 10 and BC is 10 and ac is 20
To find the lengths of AB, BC, and AC, we can use the concept of a midpoint.
Since B is the midpoint of segment AC, we can set up an equation using the Midpoint Formula:
Midpoint = (x₁ + x₂)/2 , (y₁ + y₂)/2
In this case, the coordinates of point B represent the midpoint, and the coordinates of points A and C represent the endpoints.
Let's assign a value to x and solve for AB, BC, and AC:
Let x = 1, for example.
AB = 5x = 5(1) = 5
BC = 3x + 4 = 3(1) + 4 = 7
AC = AB + BC = 5 + 7 = 12
Therefore, AB = 5, BC = 7, and AC = 12 when x is 1.
To find the lengths of AB, BC, and AC, you need to use the given information that B is the midpoint of segment AC and the expressions for AB and BC.
Since B is the midpoint of segment AC, it means that AB and BC have equal lengths. So we can set up an equation to represent this:
AB = BC
Now, let's substitute the expressions for AB and BC into the equation:
5x = 3x + 4
To solve for x, we can start by subtracting 3x from both sides:
5x - 3x = 3x + 4 - 3x
2x = 4
Next, we divide both sides of the equation by 2 to solve for x:
2x/2 = 4/2
x = 2
Now that we have the value of x, we can substitute it back into the expressions for AB and BC to find the lengths of these segments:
AB = 5x = 5(2) = 10
BC = 3x + 4 = 3(2) + 4 = 6 + 4 = 10
So, AB = 10, BC = 10, and since B is the midpoint of AC, AC = 2AB = 2(10) = 20.