Final answer:
The distance between points X(-4,7) and Y(13,-85) is found using the distance formula, resulting in √8753, which corresponds to answer choice A.
Step-by-step explanation:
The student is asking to find the distance between two points in the Cartesian plane. The distance formula derived from the Pythagorean theorem is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates. Specifically, if you have points X(x1, y1) and Y(x2, y2), the distance d between these points is calculated using the formula d = √((x2 - x1)2 + (y2 - y1)2).
To determine the distance between point X(-4,7) and point Y(13,-85), we substitute the values into the distance formula:
d = √((13 - (-4))2 + (-85 - 7)2)
= √((13 + 4)2 + (-92)2)
= √(172 + 8464)
= √(289 + 8464)
= √8753
So, the correct answer is A) √8753.