Final answer:
The distance between the points X(-4, 7) and Y(13, -8) is approximately 22.67 units, calculated using the distance formula derived from the Pythagorean Theorem.
Step-by-step explanation:
The distance between two points in a coordinate system can be calculated using the distance formula, which is derived from the Pythagorean Theorem. In this case, to find the distance between the points X(-4, 7) and Y(13, -8), we can use the following formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Inserting the given coordinates into the formula:
Distance = √[(13 - (-4))^2 + (-8 - 7)^2]
Distance = √[(13 + 4)^2 + (-15)^2]
Distance = √[17^2 + (-15)^2]
Distance = √[289 + 225]
Distance = √[514]
Distance ≈ 22.67 units
This calculation gives you the straight-line distance between the two points in the Cartesian plane.