From the given graph AB
Length of the segment AB is \(8\sqrt{2} units\)
Coordinates of the midpoint is (6,1)
Given : A is (10,5) and B is (2,-3)
To find out the length of the line segment we use distance formula
distance =\(D=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
A is (x1,y1)=(10,5)
Bis (x2,y2) =(2,-3)
Substitute the values inside the formula
\(AB=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\AB=\sqrt{\left(2-10\right)^2+\left(-3-5\right)^2}\\\\AB=\sqrt{\left(-8\right)^2+\left(-8\right)^2}\\AB=\sqrt{128} \\AB=8\sqrt{2}\)
Length of the segment AB is \(8\sqrt{2} units\)
Now we find midpoint using midpoint formula
\(\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\left(\frac{2+10}{2},\:\frac{-3+5}{2}\right)\\(6,1)\)
Coordinates of the midpoint is (6,1)
Learn more : brainly.com/question/17725325
