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

Explanation:

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

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

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