If the coordinates of point A are (x, y) and point B are (x+4, y+3), what is the

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Question: If the coordinates of point A are (x, y) and point B are (x+4, y+3), what is the distance AB?

Options:

Correct Answer: √34

Solution:

Using the distance formula: d = √((x+4 - x)² + (y+3 - y)²) = √(4² + 3²) = √(16 + 9) = √25 = 5.

If the coordinates of point A are (x, y) and point B are (x+4, y+3), what is the distance AB?

If the coordinates of point A are (x, y) and point B are (x+4, y+3), what is the distance AB?

Step 1: Identify the coordinates of point A, which are (x, y).
Step 2: Identify the coordinates of point B, which are (x+4, y+3).
Step 3: Use the distance formula, which is d = √((x2 - x1)² + (y2 - y1)²).
Step 4: Substitute the coordinates of point A and point B into the formula: d = √(((x+4) - x)² + ((y+3) - y)²).
Step 5: Simplify the expression: d = √((4)² + (3)²).
Step 6: Calculate (4)², which is 16, and (3)², which is 9.
Step 7: Add the results: 16 + 9 = 25.
Step 8: Take the square root of 25, which is 5.
Step 9: Conclude that the distance AB is 5.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).
Coordinate Geometry – Understanding how to manipulate and interpret coordinates in a 2D space.