points a b and c are collinear if the distance from point a to point b is 8 more than twice the distance from point b to point c and the length of segment ac is 5 times the length of segment of bc, how long is segment ac
Make a sketch.
From "length of segment ac is 5 times the length of segment of bc" it is clear that AC is the longer part.
So call the endpoints of your line A and C and place B between them (doesn't really have to be to scale)
label BC = x
then AC = 5x
and AB = 4x
then it said , " the distance from point a to point b is 8 more than twice the distance from point b to point c " or
AB = 2(BC) + 8
4x = 2x + 8
2x = 8
x = 4
then AC = 5x = 20
check:
By my definitions,
BC = 4
AC =20
AB = 16
is 16 equal to 8 more than 2x4 ? YES!
AB= 3x+3 AB=-1+2x and BC=11 find x
AC=21,AB=18+x,BC=x+15. Find X
To find the length of segment AC, we need to understand the given information and use it to derive the solution.
Let's assign variables to the distances between the points:
- Let dAB represent the distance between point A and point B.
- Let dBC represent the distance between point B and point C.
- Let dAC represent the distance between point A and point C.
According to the given information, we have two conditions:
1. "The distance from point A to point B is 8 more than twice the distance from point B to point C."
This can be expressed as:
dAB = 2 * dBC + 8
2. "The length of segment AC is 5 times the length of segment BC."
This can be expressed as:
dAC = 5 * dBC
Now we have two equations, allowing us to solve for the values:
Equation 1: dAB = 2 * dBC + 8
Equation 2: dAC = 5 * dBC
To find dAC, we can substitute the value of dBC from Equation 2 into Equation 1:
dAB = 2 * (dAC/5) + 8
Next, we can simplify this equation:
dAB = (2/5) * dAC + 8
Now we can isolate dAC:
dAB - 8 = (2/5) * dAC
Multiply both sides by 5/2:
(5/2) * (dAB - 8) = dAC
Simplifying this equation, we get:
(5/2) * dAB - 20 = dAC
Therefore, the length of segment AC is (5/2) * the distance between point A and point B, minus 20.