Final answer:
To find the distance between points A(-2,9) and B(12,23), the distance formula is applied, resulting in a distance of 2√98 units.
Step-by-step explanation:
The question asks for the distance between point A(-2,9) and point B(12,23). To find this, we calculate the distance between two points using the distance formula, which is derived from the Pythagorean theorem and is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the coordinates of points A and B, we get:
d = √((12 - (-2))² + (23 - 9)²)
d = √((12 + 2)² + (14)²)
d = √(14² + 14²)
d = √(196 + 196)
d = √(392)
d = √(4 × 98)
d = 2√98
So the distance between point A and point B is 2√98 units.