Question

3. Using the general graph of the triangle PQR below, fill out the table. 2 points for each, 1 point for the multiple choice question.

Answer 1

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

$\left(\dfrac{x_P+x_Q}{2},\dfrac{y_P+y_Q}{2}\right)=\left(\dfrac{0+2b}{2},\dfrac{0+2c}{2}\right)=(b,c).$

2. If X is a midpointt of the segment RQ, then its coordinates are

$\left(\dfrac{x_R+x_Q}{2},\dfrac{y_R+y_Q}{2}\right)=\left(\dfrac{2a+2b}{2},\dfrac{0+2c}{2}\right)=(a+b,c).$

3. The slope of the line passing through the points X and Y is

$\dfrac{y_Y-y_X}{x_Y-x_X}=\dfrac{c-c}{a+b-b}=\dfrac{0}{a}=0.$

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).