Answer:
1. (b,c)
2. (a+b,c)
3. 0
4. 0
5. midsegment
Step-by-step explanation:
1. If X is a midpointt of the segment PQ, then its coordinates are
[tex]\left(\dfrac{x_P+x_Q}{2},\dfrac{y_P+y_Q}{2}\right)=\left(\dfrac{0+2b}{2},\dfrac{0+2c}{2}\right)=(b,c).[/tex]
2. If X is a midpointt of the segment RQ, then its coordinates are
[tex]\left(\dfrac{x_R+x_Q}{2},\dfrac{y_R+y_Q}{2}\right)=\left(\dfrac{2a+2b}{2},\dfrac{0+2c}{2}\right)=(a+b,c).[/tex]
3. The slope of the line passing through the points X and Y is
[tex]\dfrac{y_Y-y_X}{x_Y-x_X}=\dfrac{c-c}{a+b-b}=\dfrac{0}{a}=0.[/tex]
4. Since lines XY and PR are parallel, then they have the same slopes. Thus, the slope of the line PR is 0.
Question 2. You are right, XY is a midsegment (by definition).
