To find the distance between two points in a Cartesian plane, we use the distance formula, which is derived from the Pythagorean theorem. The formula is:
d = √((x2 – x1)² + (y2 – y1)²)
Here, (x1, y1) and (x2, y2) are the coordinates of the two points. For our points (2, 4) and (4, 6):
- x1 = 2, y1 = 4
- x2 = 4, y2 = 6
Now we can plug these values into the distance formula:
- Calculate (x2 – x1):
- (4 – 2) = 2
- Calculate (y2 – y1):
- (6 – 4) = 2
- Now, substitute these results back into the formula:
- d = √((2)² + (2)²)
- d = √(4 + 4)
- d = √8
- d = 2√2
So, the distance between the points (2, 4) and (4, 6) is 2√2, which is approximately 2.83 when calculated numerically.