Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3). Round your answer to the ne

Question

bezimeni

2 months ago

11

Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3). Round your answer to the ne

arest hundredth when necessary.

Mathematics

2 answers:

Svet_ta [12.7K] · Answer 1 · 2026-03-10T03:13:06+03:00

Svet_ta [12.7K]2 months ago

4 0

Answer: 20

I completed the test and answered correctly.

tester [12.3K] · Answer 2 · 2026-03-10T03:11:38+03:00

Answer: 20 units

Step-by-step explanation:

The formula for calculating the distance between two coordinates P(a,b) and Q(c,d) is as follows:-

$PQ=\sqrt{(d-b)^2+(c-a)^2}$

Initially provided: The coordinates of the quadrilateral's vertices are C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

The distance between vertices C (−2, 1) and D (2, 4) is as follows:-

$CD=\sqrt{(4-1)^2+(2-(-2))^2}\\\\\Rightarrow\ CD=\sqrt{(3)^2+(4)^2}\\\\\Rightarrow\ CD=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ CD=5\text{ units}$

Distance between points D (2, 4) and E (5, 0) is calculated as:-

$DE=\sqrt{(4-0)^2+(2-5)^2}\\\\\Rightarrow\ DE=\sqrt{(4)^2+(-3)^2}\\\\\Rightarrow\ DE=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ DE=5\text{ units}$

Distance between coordinates E (5, 0) and F (1, −3) is given by:-

$EF=\sqrt{(-3-0)^2+(1-5)^2}\\\\\Rightarrow\ EF=\sqrt{(-3)^2+(-4)^2}\\\\\Rightarrow\ EF=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ EF=5\text{ units}$

Distance from C (−2, 1) to F (1, −3) is as follows:-

$FC=\sqrt{(-3-1))^2+(1-(-2))^2}\\\\\Rightarrow\ FC=\sqrt{(-4)^2+(3)^2}\\\\\Rightarrow\ FC=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ FC=5\text{ units}$

The total perimeter of the quadrilateral is calculated as = CD + DE + EF + FC

$=5+5+5+5=20\text{ units}$