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.
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 solve this step by step:
Step 1: Determine the position of point K on segment AB.
Since point K is 5 cm closer to point A than to point B, we can divide the segment into two parts such that KB is 5 cm longer than KA.
Step 2: Express AK and KB in terms of a single variable.
Let's assume that KA is x cm. Therefore, KB would be x + 5 cm.
Step 3: Write an equation related to the total length of segment AB.
The total length of segment AB is 12 cm, so we can write the equation as:
AK + KB = 12
Step 4: Substitute the expressions for AK and KB from step 2 into the equation from step 3.
x + (x + 5) = 12
Step 5: Simplify and solve for x.
2x + 5 = 12
2x = 12 - 5
2x = 7
x = 7/2
x = 3.5
Step 6: Calculate the values of AK and KB.
AK = 3.5 cm
KB = 3.5 + 5 = 8.5 cm
Therefore, AK is 3.5 cm and BK is 8.5 cm.