Given: the coordinates of triangle pqr are p(0, 0), q(2a, 0), and r(2b, 2c). prove: the line containing the midpoints of two sides of a triangle is parallel to the third side. as part of the proof, find the midpoint of pq

Step-by-step explanation:

Given: In ΔPQR, the coordinates of the vertices are P(0, 0), Q(2a, 0), and R(2b, 2c).

To prove: The line containing the midpoints of two sides of a triangle is parallel to the third side.

Proof: In ΔPQR, the coordinates of the vertices are P(0, 0), Q(2a, 0), and R(2b, 2c).

Let, A, B and C be the mid-points of PQ, PR and QR respectively. Thus, the coordinates of S are:

The coordinates of B are:

And the coordinates of C are:

Now, slope of AB is given as:

And slope of QR is given as:

Since the slopes of AB and QR are equal, hence they must be parallel.

Hence proved.

Also, Since A is the midpoint of PQ, therefore teh coordinates are:

A=

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step-by-step explanation: