let ABC be a triangle and let p be the midpoint of side AB

let and

express and in terms of and and

hence prove that the midpoint of the hypotenuse of a right-angle triangle is equidistant from the three vertices

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let p be the plane with cartesian equation 2x+y-3z=9 and let A,B be points with coordinates (1,-2,3) and (-2,1,-1)

l is the line passing through the point A and B

find the coordinates of the point C where the line l intersects the plane p

i have no ideas how to find the intersection between a line and a plane

thx