Find the perimeter of a regular heptagon with consecutive vertices at "A" (-2,-5) and "B" (1,-9)

Mathematics

1 answer:

weqwewe [10]3 years ago

7 0

Answer:

Perimeter is 35 units.

Step-by-step explanation:

A heptagon has 7 equal sides.

Given the length of two consecutive vertices, A(-2-5) and B(1,-9).

We can find the length of AB and multiply by 7.

Recall the distance formula;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of AB is

$|AB|=\sqrt{(-2-1)^2+(-5--9)^2}$

$|AB|=\sqrt{(-3)^2+(4)^2}$

$\Rightarrow |AB|=\sqrt{9+16}$

$\Rightarrow |AB|=\sqrt{25}$

$\Rightarrow |AB|=5\:units$

Therefore the perimeter is $7\times 5=35\:units$ .

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