The perimeter of a △ABC equals 12 in. The midpoints of the sides M, N and K are connected consecutively. Find the perimeter of △
1 answer:
Answer:
6 inches
Step-by-step explanation:
Triangle midline theorem: In a triangle, the midline joining the midpoints of two sides is parallel to the third side and half as long.
Points M, N and K are midpoints of the sides AB, BC and AC. Acording to the Triangle midline theorem,
The perimeter of the triangle MNK is
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Make a change of coordinates:
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
to 
. To do this, notice that
we need to take the reciprocal of the Jacobian above.
The integral then changes to
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
we need to take the reciprocal of the Jacobian above.
The integral then changes to