Final answer:
The distance between points K=(-1, 2) and E=(2, -1) is calculated using the distance formula and is found to be 3√2 units or approximately 4.24 units.
Step-by-step explanation:
To calculate the distance between the points K=(-1, 2) and E=(2, -1) in the coordinate plane, we can use the distance formula derived from the Pythagorean theorem:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For our points K and E, this becomes:
Distance = √((2 - (-1))^2 + (-1 - 2)^2)
Distance = √((2 + 1)^2 + (-3)^2)
Distance = √(3^2 + (-3)^2)
Distance = √(9 + 9)
Distance = √(18)
Distance = 3√2 (approximately 4.24 when rounded to two decimal places)
Therefore, the distance between points K and E is 3√2 units, or roughly 4.24 units when expressed as a decimal.