Question
The Length of segment AB is 12 cm. Point K is on segment AB and it is 5 cm closer to point A than to point B. Find AK and BK.
Answers
Answered by
GPT 3.5
To find AK and BK, we can use the concept of midpoint.
Let's say AK = x cm. Since K is 5 cm closer to point A than to point B, BK can be represented as AK + 5 cm.
According to the midpoint formula, the midpoint of AB is equal to (A + B)/2. Since the length of segment AB is 12 cm, the midpoint would be 6 cm.
So, (A + B)/2 = 6.
Simplifying, we get A + B = 12.
Now, we substitute AK and BK into the equation:
AK + BK = 12.
Plugging in AK = x, and BK = x + 5, we get:
x + (x + 5) = 12.
Combining like terms, we have:
2x + 5 = 12.
Subtracting 5 from both sides:
2x = 7.
Dividing both sides by 2, we find:
x = 3.5.
Therefore, AK = 3.5 cm and BK = 3.5 + 5 = 8.5 cm.
Let's say AK = x cm. Since K is 5 cm closer to point A than to point B, BK can be represented as AK + 5 cm.
According to the midpoint formula, the midpoint of AB is equal to (A + B)/2. Since the length of segment AB is 12 cm, the midpoint would be 6 cm.
So, (A + B)/2 = 6.
Simplifying, we get A + B = 12.
Now, we substitute AK and BK into the equation:
AK + BK = 12.
Plugging in AK = x, and BK = x + 5, we get:
x + (x + 5) = 12.
Combining like terms, we have:
2x + 5 = 12.
Subtracting 5 from both sides:
2x = 7.
Dividing both sides by 2, we find:
x = 3.5.
Therefore, AK = 3.5 cm and BK = 3.5 + 5 = 8.5 cm.