M and N are the midpoints of PR(which has a line over PR) and QR(which has a line over QR)respectively. Using graph paper, repeat this process from the last problem using different coordinates for P, Q, and R. How do these lengths MN and PQ compare now? What do you think you can conclude about the lengths of these segments? (In your answer, make sure to include your coordinates for all points, the lengths of the segments, and your conclusion.) I sent the prior question to this question but I haven't received any response yet. I'm going to re-evalute the 1st part of the question. Thank you Daman

Question

M and N are the midpoints of PR(which has a line over PR) and QR(which has a line over QR)respectively. Using graph paper, repeat this process from the last problem using different coordinates for P, Q, and R. How do these lengths MN and PQ compare now? What do you think you can conclude about the lengths of these segments? (In your answer, make sure to include your coordinates for all points, the lengths of the segments, and your conclusion.) I sent the prior question to this question but I haven't received any response yet. I'm going to re-evalute the 1st part of the question. Thank you Daman

Answer 1

Are you referring to this question?

http://www.jiskha.com/display.cgi?id=1311726747

Once you find N, find the slope of MN, it should be the same as the slope of the base, so the lines would be parallel.
The length of the line MN should be exactly 1/2 of the length of the base.

Obviously we cannot help you with the graphing part of the question.

Answer 2

To compare the lengths of MN and PQ, let's start by understanding the steps involved in finding these lengths.

1. First, we need to choose different coordinates for points P, Q, and R. Let's assume the following coordinates:

P (x1, y1)
Q (x2, y2)
R (x3, y3)

2. Next, we need to find the midpoints M and N. The midpoint formula is given by:

M = ((x1 + x3) / 2, (y1 + y3) / 2)
N = ((x2 + x3) / 2, (y2 + y3) / 2)

3. Once we have the coordinates of M and N, we can calculate the lengths of MN and PQ using the distance formula. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of MN and PQ using the new coordinates and draw a conclusion based on the results.

Suppose for the new example, we have the following coordinates:
P (1, 2)
Q (4, 6)
R (7, 4)

Calculating the midpoints, we have:
M = ((1 + 7) / 2, (2 + 4) / 2) = (4, 3)
N = ((4 + 7) / 2, (6 + 4) / 2) = (5.5, 5)

Now, let's use the distance formula to find the lengths MN and PQ.

For MN:
d = sqrt((5.5 - 4)^2 + (5 - 3)^2)
= sqrt(1.5^2 + 2^2)
= sqrt(2.25 + 4)
= sqrt(6.25)
≈ 2.5

For PQ, we need to calculate the distance between points P and Q:
d = sqrt((4 - 1)^2 + (6 - 2)^2)
= sqrt(3^2 + 4^2)
= sqrt(9 + 16)
= sqrt(25)
= 5

Comparing the lengths MN and PQ, MN is approximately 2.5, while PQ is 5. Therefore, we can conclude that the length of PQ is twice the length of MN.

Overall, based on our calculations, when finding the midpoints of different coordinates, the length of PQ is always double the length of MN.