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given: the coordinates of triangle PQR are (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 scale.
as part of the proof find the midpoint of QR


A) (a-b,c)
B) (a+b,c)
C) (a,c)
D) (b,c)

Respuesta :

meerkat18
In your question where a triangle PQR having a coordinates of P(0,0), Q(2a,0), and R(2b,2c) to prove that the line containing the midpoint of two sides of a triangle is parallel to the third scale the midpoit of QR should be letter B. (a+b, c)

Answer: The midpoint of QR has co-ordinates [tex](a+b,c)[/tex].


Step-by-step explanation: In ΔPQR, the coordinates of the vertices are [tex]P(0,0),~Q(2a,0) ~\textup{and}~ R(2b,2c)[/tex].

Let, S, T  and V be the mid-points of PQ, PS and QS respectively. Thus, the coordinates of S are [tex]\left ( \frac{0+2a}{2},\frac{0+0}{2} \right )=(a,0)[/tex]

and coordinates of T are [tex]\left ( \frac{0+2b}{2},\frac{0+2c}{2} \right )=(b,c)[/tex].

Now, slope of line ST is [tex]\frac{c-0}{b-a}=\frac{c}{b-a}[/tex]

and slope of QR is [tex]\frac{2c-0}{2b-2a}=\frac{c}{b-a}[/tex].

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

Also, coordinates of V are [tex]\left ( \frac{2a+2b}{2},\frac{0+2c}{2} \right )=(a+b,c)[/tex].

 

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