Дано: C (-3; m), D (5; 1), F (-11; 5), DC=CF Найдите m

Находим квадраты длин.

DC^2 = (Dx - Cx) ^2 + (Dy - Cy) ^2 = (5 + 3) ^2 + (1 - m) ^2 = (m - 1) ^2 + 8^2

CF^2 = (Cx - Fx) ^2 + (Cy - Fy) ^2 = (-3 + 11) ^2 + (m - 5) ^2 = (m - 5) ^2 + 8^2

Квадраты длин равны.

(m - 1) ^2 + 8^2 = (m - 5) ^2 + 8^2

(m - 1) ^2 - (m - 5) ^2 = 0

((m - 1) - (m - 5)) ((m - 1) + (m - 5)) = 0

4 * (2m - 6) = 0

2m - 6 = 0

m = 3