Final answer:
The length between points A(-6,1) and B(9,-11) is approximately 19.2 units. The midpoint of the line segment AB is (1.5, -2.5)
Step-by-step explanation:
The length of a line segment can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of points A(-6,1) and B(9,-11), we can substitute the values into the formula to find the length:
d = sqrt((9 - (-6))^2 + (-11 - 1)^2) = sqrt((15)^2 + (-12)^2) = sqrt(225 + 144) = sqrt(369) = approximately 19.2 units
To find the midpoint, we can use the midpoint formula:
M = ( (x1 + x2)/2, (y1 + y2)/2 )
Substituting the values of points A and B:
M = ( (-6 + 9)/2, (1 + (-11))/2 ) = (3/2, -5/2) = (1.5, -2.5)