Final answer:
The distance between endpoints E(2, -3) and F(-5, -6) is calculated using the distance formula derived from the Pythagorean theorem, resulting in approximately 7.6 units when rounded to the nearest tenth.
Step-by-step explanation:
To find the distance between the endpoints E(2, -3) and F(-5, -6), we use the distance formula, which is derived from the Pythagorean theorem. This formula is: distance = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points E(2, -3) and F(-5, -6) into the formula:
distance = √[(-5 - 2)² + (-6 + 3)²] = √[(-7)² + (-3)²] = √[49 + 9] = √[58]
The square root of 58 is approximately 7.6, so the distance EF is approximately 7.6 units when rounded to the nearest tenth.