Final answer:
The distance between points E (3, -4) and F (-3, 8) is calculated using the distance formula, resulting in an exact and simplified distance of √(180), which is equal to 6√5. This approximates to 13 units, which corresponds to option C: EF = 13.
Step-by-step explanation:
The distance between two points E (3, − 4) and F (−3, 8) in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: √D = √((x2 − x1)² + (y2 − y1)²).
Substituting the coordinates of E and F into the formula, the calculation is as follows:
√D = √((−3 − 3)² + (8 − (−4))²) = √((−6)² + (12)²) = √(36 + 144) = √180 = √(36 × 5) = 6√5.
Since 6√5 is an exact and simplified form, we need to match it with the given options. The exact decimal value of 6√5 is approximately 13.42, which corresponds closest to option C: EF = 13. Therefore, the distance between points E and F is 13 units.