Question

Find the midpoint and distance of AB given
A(2,4) and B(4,8)

Answer 1

Answer: midpoint=(3,6)    distance of AB=2√5

Step-by-step explanation:

$\displaystyle\\A(2,4)\ \ \ \ B(4,8)\\\boxed {the\ midpoint\ C_x=\frac{x_A+x_B}{2} }\\Hence,\\C_x=\frac{2+4}{2} \\\\C_x=\frac{6}{2} \\\\C_x=3$

$\displaystyle\\\boxed {the\ midpoint\ C_y=\frac{y_A+y_B}{2} }\\Hence,\\C_x=\frac{4+8}{2} \\\\C_x=\frac{12}{2} \\\\C_y=6\\Thus,\ \ (3,6)$

$\displaystyle\\\\\boxed {L_{AB}=\sqrt{(x_B-x_A)^2+((y_B-y_A)^2} }\\\\L_{AB}=\sqrt{(4-2)^2+(8-4)^2} \\\\L_{AB}=\sqrt{2^2+4^2} \\\\L_{AB}=\sqrt{4+16} \\\\L_{AB}=\sqrt{20} \\\\L_{AB}=\sqrt{4*5} \\\\L_{AB}=\sqrt{2^2*5}\\\\L_{AB}=2\sqrt{5}$