Answer:
D. Place the triangle on a coordinate grid such that QR lies on the x-axis and PQ lies in the y-axis
Step-by-step explanation:
A midsegment of the triangle is the line segment the connects the midpoints of two sides of the triangle. This midsegmet is parallel to the base.
Constructing a triangle with two sides over the x-axis and y-axis respectively makes it easier to verify that the midsegment is half the base.
So, it's D. The best option.
I suppose
The vectors that span form a basis for
if they are (1) linearly independent and (2) any vector in
can be expressed as a linear combination of those vectors (i.e. they span
).
Compute the Wronskian determinant:
The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of is 3.
Write an arbitrary vector in as
. Then the given vectors span
if there is always a choice of scalars
such that
which is equivalent to the system
The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives
so the vectors do span .
The vectors comprising form a basis for it because they are linearly independent.