Find the vector AB presented by the directed line segment with initial point A(1, 2) and terminal point B(4, 6). Find the length of the line segment joining A and B.
To find the vector AB presented by the directed line segment with initial point A(1, 2) and terminal point B(4, 6), we subtract the coordinates of A from the coordinates of B
To find the vector AB presented by the directed line segment with initial point A(1, 2) and terminal point B(4, 6), we subtract the coordinates of A from the coordinates of B.
The vector AB is given by:
AB = (4, 6) – (1, 2)
To perform the subtraction, we subtract the corresponding components:
AB = (4 – 1, 6 – 2)
= (3, 4)
Therefore, the vector AB is (3, 4).
To find the length of the line segment joining A(1, 2) and B(4, 6), we use the distance formula.
The distance formula is given by:
d = √((x2 – x1)^2 + (y2 – y1)^2)
Plugging in the coordinates of A and B, we have:
d = √((4 – 1)^2 + (6 – 2)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √(25)
= 5
Therefore, the length of the line segment joining A and B is 5.
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