M and N are the midpoints ofandrespectively.
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.)
(its a triangle)
To compare the lengths MN and PQ, we need to perform the same process as in the previous problem but with different coordinates for points P, Q, and R.
Let's assume the following coordinates for the vertices of the triangle:
- Point A: (x1, y1)
- Point B: (x2, y2)
- Point C: (x3, y3)
Now, let's calculate the coordinates for points P, Q, and R using the midpoints formula:
- Point P: ( (x1 + x2)/2 , (y1 + y2)/2 )
- Point Q: ( (x2 + x3)/2 , (y2 + y3)/2 )
- Point R: ( (x3 + x1)/2 , (y3 + y1)/2 )
Once you have the coordinates for points P, Q, and R, you can plot them on the graph paper.
Next, calculate the lengths of segments MN and PQ.
- Length of MN: √((x1 - x2)^2 + (y1 - y2)^2)
- Length of PQ: √((x1 - x3)^2 + (y1 - y3)^2)
After calculating the lengths of MN and PQ, compare them. If MN is equal to PQ, then you can conclude that the lengths of these segments are equal. If MN is not equal to PQ, then you can conclude that the lengths of these segments are not equal.
Make sure to substitute the given coordinates for A, B, and C to find the specific lengths of MN and PQ, and then use that information to reach your conclusion.