Final answer:
To calculate the exact distance between the points (1,4) and (-2,-5), you apply the distance formula which is d = √[(x2 - x1)² + (y2 - y1)²], yielding an answer of 3√10 units.
Step-by-step explanation:
Finding the Distance Between Two Points
To find the exact distance between two points (1,4) and (-2,-5) in the Cartesian plane, we use the distance formula derived from the Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is calculated as:
d = √[(x2 - x1)² + (y2 - y1)²]
Applying the formula to the given points:
d = √[(-2 - 1)² + (-5 - 4)²]
= √[(-3)² + (-9)²]
= √[9 + 81]
= √90
= 3√10
The exact distance between the points (1,4) and (-2,-5) is therefore 3√10 units.