Final answer:
To find the length of line segment Y, use the distance formula with the two given points X(-9, 2) and Y(5, -4). The calculation yields √((5 - (-9))² + (-4 - 2)²), which simplifies to approximately 15.23 when rounded to the nearest hundredth.
Step-by-step explanation:
The question asks to find the length of line segment Y given two points, X(-9, 2) and Y(5, -4). This can be solved by using the distance formula, which is derived from the Pythagorean theorem. To calculate the distance between the two points, the formula is √((x2-x1)² + (y2-y1)²). Substituting the given coordinates into the formula results in:
√((5 - (-9))² + (-4 - 2)²)
= √((5 + 9)² + (-6)²)
= √(14² + (-6)²)
= √(196 + 36)
= √(232)
When you calculate the square root of 232 and round to the nearest hundredth, you get approximately 15.23. Thus, the length of line segment Y is about 15.23 units.