Question

弦长公式;AB=√(1+k^2)*│x1-x2│=│y1-y2│√[(1/k^2)+1](求过程)

Answer 1

A(x1,y1) B(x2,y2)

k=(y1-y2)/(x1-x2)

k^2=(y1-y2)^2/(x1-x2)^2

(y1-y2)^2=k^2(x1-x2)^2

(x1-x2)^2=(y1-y2)^2/k^2

|AB|=√[(x1-x2)^2+(y1-y2)^2]

=√[(x1-x2)^2+k^2(x1-x2)^2]

=|x1-x2|√(1+k^2)

|AB|=√[(x1-x2)^2+(y1-y2)^2]

=√[(y1-y2)^2/k^2+(y1-y2)^2]

=|y1-y2|√(1/k^2+1)