How do I find perimeter of the figure with the given vertices? Confused here!

Question

D(0,1),E(5,4) and F(2,6)

Answer 1

Since three vertices are given, the figure must be a triangle. To find the perimeter, you must find the lengths of all three sides and add them up. The lengths can be found using the distance formula:

 

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

 

The lengths of the three sides using this formula are:

 

DE = √34

EF = √13

DF = √34 .

 

Thus, the perimeter is P = 2√34 + √13 . Notice that the triangle is isosceles since two of the sides have equal lengths.

 

If you need a decimal answer, you should use a calculator.

Answer 2

Dear Claudia,

 

Let me get you started on this. Vertices are just corners, and because there are only three points, you can be sure it's a triangle. We know that a perimeter is the sum of the lengths of all the sides. There are three. How can you find side lengths? Do you remember the distance formula? (Hint: the distance formula for length between two coordinate points.)

1. apply it to points D & E = side one
2. then same for D & F = side two
3. then lastly for E & F =side three
4. add all your results for the three sides => perimeter!

It sounded trickier than it was, but this problem is a lot of work with a lot of calculations. Hope this helps. Let me know if you need to see a calculation of one of the sides.

 

~Best,

Marina