A is the midpoint of CT. CA= 3x+6 and CT= 24, find x
X=2
Since A is the midpoint of CT, we know that CA is half of CT. Therefore, we have the equation:
CA = 1/2 * CT
Substituting the given values into the equation:
3x + 6 = 1/2 * 24
Now, let's solve for x:
Multiply both sides of the equation by 2:
2(3x + 6) = 24
Distribute the 2 to the terms inside the parentheses:
6x + 12 = 24
Subtract 12 from both sides of the equation:
6x = 24 - 12
Simplify:
6x = 12
Divide both sides of the equation by 6:
x = 12/6
Simplify:
x = 2
Therefore, the value of x is 2.
To find the value of x, we need to use the midpoint formula, which states that the coordinates of the midpoint of a line segment are equal to the average of the coordinates of the endpoints.
In this case, A is the midpoint of CT, so we can set up the following equation:
CA + AT = CT
Given that CA is 3x + 6 and CT is 24, we have:
3x + 6 + AT = 24
To find AT, let's rearrange the equation:
AT = 24 - (3x + 6)
AT = 24 - 3x - 6
AT = 18 - 3x
Now, since A is the midpoint, AT is equal to TA. Therefore, we can rewrite the equation as:
18 - 3x = 3x + 6
Let's solve for x:
18 - 6 = 3x + 3x
12 = 6x
x = 12/6
x = 2
Therefore, the value of x is 2.