Question

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

Answer 1

Answer:

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:

$A=(\frac{0+2a}{2},\frac{0+0}{2})=(a,0)$

The coordinates of B are:

$B=(\frac{0+2b}{2},\frac{0+2c}{2})=(b,c)$

And the coordinates of C are:

$C=(\frac{2a+2b}{2},\frac{0+2c}{2})=(a+b,c)$

Now, slope of AB is given as:

$s={\frac{c-0}{b-a}}={\frac{c}{b-a}}$

And slope of QR is given as:

$s={\frac{2c-0}{2b-2a}}={\frac{c}{b-a}}$

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=$(\frac{0+2a}{2},\frac{0+0}{2})=(a,0)$

Answer 2

Answer:

The answer is (a, 0)

Step-by-step explanation:

It's correct.