Points EC bisects points AD at C. For each of the following, find the value of 'x' and the measure of the indicated segment. Please correct me if I'm wrong!
1. AC= 3x+6 and CD=2x+14
x=_______
AC=______
Answer: x=8
AC= 30
2. AC= 5x-8 and CD=16-3x
x=______
AD=_____
Answer: x=3
What will AD be because I'm sooo confused on how to work it out..
3. AD= 6x-4 and AC=4x-3
x=_______
CD______
Answer: x= .5
CD= I'm confused how you do this one too
4. AC=3x-1 and AD= 12-x
x=_____
CD=____
Answer: x= -3.25
CD= I'm have trouble working this one out too
1. To find the value of 'x' and the measure of AC, we know that AC bisects AD at point C. This means that AC and CD are equal in length. We can set up an equation to solve for 'x'.
3x + 6 = 2x + 14
Now, we can solve for 'x':
3x - 2x = 14 - 6
x = 8
To find AC, we can substitute the value of 'x' back into the AC equation:
AC = 3(8) + 6
AC = 30
So, the value of 'x' is 8 and the measure of AC is 30.
2. Similar to the previous question, we know that AC bisects AD at point C. This means AC = CD. Let's set up the equation:
5x - 8 = 16 - 3x
Now, solve for 'x':
5x + 3x = 16 + 8
8x = 24
x = 3
To find the length of AD, we substitute the value of 'x' back into the AD equation:
AD = 12 - 3
AD = 9
So, the value of 'x' is 3 and the measure of AD is 9.
3. Following the same pattern, we can set up the equation:
6x - 4 = 4x - 3
Solve for 'x':
6x - 4x = -3 + 4
2x = 1
x = 0.5
To find the length of CD, we substitute the value of 'x' back into the CD equation:
CD = 2(0.5) + 14
CD = 15
So, the value of 'x' is 0.5 and the measure of CD is 15.
4. Once again, AC bisects AD at point C. We set up the equation:
3x - 1 = 12 - x
Solve for 'x':
3x + x = 12 + 1
4x = 13
x = 13/4 = -3.25
To find CD, we substitute the value of 'x' back into the CD equation:
CD = 12 - (-3.25)
CD = 15.25
So, the value of 'x' is -3.25 and CD is 15.25.