The length of the line segment joining the points (x1, y1) and (x2, y2) is given by sqrt[(x1 - x2)^2 + (y1 - y2)^2]

substituting the values of x and y from the points A(2, 7) and B(-3 , -12) we get:

L = sqrt [( 2 + 3)^2 +...

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The length of the line segment joining the points (x1, y1) and (x2, y2) is given by sqrt[(x1 - x2)^2 + (y1 - y2)^2]

substituting the values of x and y from the points A(2, 7) and B(-3 , -12) we get:

L = sqrt [( 2 + 3)^2 + (7 + 12)^2]

=> sqrt [ 5^2 + 19^2]

=> sqrt [ 25 + 361]

=> sqrt [ 386]

**The required length of the line segment AB is sqrt 386**

Given the line segment AB such that A(2,7) and B(-3,-12)

We need to find the length of the line AB.

Then, we will use the distance between two points formula to find the length.

We know that:

D = sqrt( x2-x1)^2 + (y2-y1)^2

==> l AB l = sqrt[ (-3-2)^2 + (-12-7)^2 ]

= sqrt[ (25 + 361)

= sqrt(386) = 19.65

**Then, the length of the line segment AB is 19.65 units ( approx.)**