MHB Is there a formula for finding the perimeter of a triangle with known vertices?

[mathdad]

The vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5).

1. Find the perimeter of triangle ABC.

I must use the distance formula for points to find the individual lengths. I then must add all 3 lengths to find the perimeter. Correct?

2. Find the perimeter of the triangle that is formed by joining the midpoints of the three sides of triangle ABC.

I MUST find the midpoint of AB, BC, and BC. I then repeat the same steps for part 1 above. Correct?

3. Compute the ratio of the perimeter on part 1 to the perimeter in part b.

Let r = ratio

r = (perimeter part 1)/(perimeter part 2)

Is this what I must solve for part 3?

4. What theorem from geometry provides the answer for part 3 without using the results in part 1 and 2.

I need help with part 4.

 

[Greg]

4. The Triangle Midpoint theorem.

 

[MarkFL]

You may wish to review these threads, as they deal with the same triangle and perimeter:

• https://mathhelpboards.com/pre-calculus-21/triangle-abc-22202.html
• https://mathhelpboards.com/pre-calculus-21/perimeter-triangle-abc-21551.html
• https://mathhelpboards.com/pre-calculus-21/perimeter-triangle-abc-21111.html

 

[mathdad]

You may wish to review these threads, as they deal with the same triangle and perimeter:

• http://mathhelpboards.com/pre-calculus-21/triangle-abc-22202.html
• http://mathhelpboards.com/pre-calculus-21/perimeter-triangle-abc-21551.html
• http://mathhelpboards.com/pre-calculus-21/perimeter-triangle-abc-21111.html

I forgot that I had posted the same question some time ago. Good. I can move on in the textbook.