Question

Find the length and the midpoind of the segment with the given endpointsA(2,3 )and B(5,7)

Answer 1

Answer:

$Suppose,~a~line~segment~has~midpoints~(x_1,y_1)~and~(x_2,y_2). Then,\\Midpoint~of~the~line = (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})\\Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\According~ to~ the ~question,\\(x_1,y_1) = A(2,3)\\(x_2,y_2) = B(5,7)\\Midpoint~of~AB = (\frac{2+5}{2},\frac{3+7}{2}) = (\frac{7}{2},5)\\AB = \sqrt{(5-2)^2+(7-3)^2} = \sqrt{3^2+4^2} = 5units$