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

1. (b,c)

2. (a+b,c)

3. 0

4. 0

5. midsegment

Explanation:

1. If X is a midpointt of the segment PQ, then its coordinates are

`\left((x_P+x_Q)/(2),(y_P+y_Q)/(2)\right)=\left((0+2b)/(2),(0+2c)/(2)\right)=(b,c).`

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

`\left((x_R+x_Q)/(2),(y_R+y_Q)/(2)\right)=\left((2a+2b)/(2),(0+2c)/(2)\right)=(a+b,c).`

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

`(y_Y-y_X)/(x_Y-x_X)=(c-c)/(a+b-b)=(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).