turning point

a point at which a decisive change takes place; critical point; crisis.

a point at which something changes direction, especially a high or low point on a graph.

Surveying. a point temporarily located and marked in order to establish the elevation or position of a surveying instrument at a new station.

Origin of turning point

First recorded in 1850–55

Marlantes, soft-spoken and earnest, recounts a turning-point moment after he returned from Vietnam.

The Last Vietnam War Epic |John Douglas Marshall |April 8, 2010 |DAILY BEAST
This turning-point appears in the simple announcement that 'Dorset has fled to Richmond.'

Shakespeare as a Dramatic Artist |Richard G. Moulton
It definitely established our supremacy of the air, and was the turning-point of the whole war.

"Over There" with the Australians |R. Hugh Knyvett
The withdrawal of protective legislation proved the turning-point in the fortunes of the British shipowner.

The Englishman in China During the Victorian Era, Vol. I (of 2) |Alexander Michie

When they reached the turning-point the woman said: "Come, let us rest for a little."

The Myths of the North American Indians |Lewis Spence
These sub-dural inoculations were the turning-point of Pasteur's discovery.

Experiments on Animals |Stephen Paget

turning point

a moment when the course of events is changed the turning point of his career

a point at which there is a change in direction or motion

maths a stationary point at which the first derivative of a function changes sign, so that typically its graph does not cross a horizontal tangent

surveying a point to which a foresight and a backsight are taken in levelling; change point