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

  • MHB
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In summary, the vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5). To find the perimeter, the distance formula can be used to find the individual lengths of the sides, which can then be added together. To find the perimeter of the triangle formed by joining the midpoints of the sides, the midpoint formula must be used for each side, and then the same steps as before can be repeated. The ratio of the perimeters in part 1 and part 2 can be found by dividing the perimeter in part 1 by the perimeter in part 2. This can also be solved using the Triangle Midpoint theorem, without using the results from parts 1
  • #1
mathdad
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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.
 
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  • #2
4. The Triangle Midpoint theorem.
 
  • #3
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
 
  • #4
MarkFL said:
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.
 

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

What is the definition of a triangle?

A triangle is a three-sided polygon with three angles. It is one of the simplest geometric shapes and is commonly used in mathematics and geometry.

How do you classify triangles based on their sides?

Triangles can be classified as equilateral, isosceles, or scalene based on the length of their sides. An equilateral triangle has three sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has no sides of equal length.

How do you classify triangles based on their angles?

Triangles can be classified as acute, right, or obtuse based on the measure of their angles. An acute triangle has all angles less than 90 degrees, a right triangle has one 90 degree angle, and an obtuse triangle has one angle greater than 90 degrees.

How do you find the area of a triangle?

The area of a triangle can be found by multiplying the base (the length of the side on which the triangle stands) by the height (the distance from the base to the opposite vertex) and dividing the result by 2. The formula for the area of a triangle is A = 1/2 * b * h.

How do you use the Pythagorean Theorem to find the missing side of a right triangle?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem can be used to find the missing side of a right triangle by solving for the unknown side using the formula c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

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