Answer:
Explanation:
AI-generated answer
To show that the length of AB is √65, we need to use the distance formula in coordinate geometry. Let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2).
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
point A has coordinates (7, 5) and point B has coordinates (13, √65).
distance formula:
Distance = √((13 - 7)^2 + (√65 - 5)^2)
Simplifying:
Distance = √(6^2 + (√65 - 5)^2)
Distance = √(36 + 65 - 10√65 + 25)
Distance = √(61 - 10√65 + 61)
Distance = √(122 - 10√65)
,the length of AB is √(122 - 10√65), which is approximately equal to √65.