To find the length of line segment AB, we first need to understand what is meant by the coordinates given: AC(4, AE(7)) and AD(10). Assuming AC(4, 7) represents the coordinates of point A, we take point A as (4, 7).
Next, we interpret AD(10) in this context. However, as it’s stated, it seems a bit unclear. If we assume that point B’s coordinates are to be determined, we might consider point B based on some relationships. For this explanation, let’s explore the case where point B is located on the x-axis at (10, 0).
Now, we apply the distance formula to find the length of line segment AB:
The distance formula is given as:
D = √[(x₂ – x₁)² + (y₂ – y₁)²]
Where:
- (x₁, y₁) are the coordinates of point A (4, 7)
- (x₂, y₂) are the coordinates of point B (10, 0)
Substituting the coordinates into the formula:
D = √[(10 – 4)² + (0 – 7)²]
Calculating each component:
- (10 – 4)² = 6² = 36
- (0 – 7)² = (-7)² = 49
Summing these values yields:
D = √[36 + 49] = √[85]
To finalize, we approximate the value of √85. This gives us the length of line segment AB:
D ≈ 9.22
Therefore, the length of line segment AB is approximately 9.22 units.