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QuestionFind the length of segment AB if points C and D are 23 and 8 units from A, respectively.

Studdy Solution

STEP 1

Assumptions1. The line segment is AB. There are two points on the line segment AB, let's call them C and D3. The distance from point A to point C is23 units4. The distance from point A to point D is8 units5. The points C and D are on the line segment AB in such a way that point D is between points A and C

STEP 2

We need to find the length of the line segment AB. Since point D is between points A and C, the length of the line segment AB is the sum of the lengths of the line segments AD and DB.
AB=AD+DBAB = AD + DB

STEP 3

We know the length of the line segment AD, which is8 units, but we don't know the length of the line segment DB. However, we know that the length of the line segment AC is23 units, and since point D is between points A and C, the length of the line segment DB is the difference between the lengths of the line segments AC and AD.
DB=AC−ADDB = AC - AD

STEP 4

Now, plug in the given values for the lengths of the line segments AC and AD to calculate the length of the line segment DB.
DB=23−8DB =23 -8

STEP 5

Calculate the length of the line segment DB.
DB=23−8=15DB =23 -8 =15

STEP 6

Now that we have the lengths of the line segments AD and DB, we can find the length of the line segment AB by adding these two lengths together.
AB=AD+DBAB = AD + DB

STEP 7

Plug in the values for the lengths of the line segments AD and DB to calculate the length of the line segment AB.
AB=+15AB = +15

STEP 8

Calculate the length of the line segment AB.
AB=8+15=23AB =8 +15 =23The length of the line segment AB is23 units.

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