Hello, ToriBori!

You're correct: the diagonals are perpendicular.

But that's not relevant to the problem . . .

A quick sketch reveals that and are the diagonals.An orienteering course has been marked by four points on a graph:

. .

a) A drink station is to be positioned at the intersection

of the diagonals of the quadrilateral OABC.

Find the coordinates of the drink station.

The slope of is: .

The line through with slope

. . has the equation: . .[1]

The slope of is: .

The line through with slope 2

. . has the equation: . .[2]

To find their intersection, equate [1] and [2]:

. .

Substitute into [2]: .

Therefore, the drink station is at: