Question

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

Answer 1

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Answer 2

Answer:

The perimeter of the quadrilateral CDEF is $( \sqrt { 10 } + \sqrt { 17 } + \sqrt { 8 } + \sqrt { 5 } )$ units.

Solution:

Using Distance Formula, we can find out length of each side.

According to Distance Formula:

$\mathrm { CD } = \sqrt { [ ( - 3 ) - ( - 2 ) ] ^ { 2 } + [ ( 1 - 4 ) ] ^ { 2 } } = \sqrt { ( - 1 ) ^ { 2 } + ( - 3 ) ^ { 2 } } = \sqrt { 1 + 9 } = \sqrt { 10 } \text { units. }$

$\mathrm { DE } = \sqrt { [ ( 1 ) - ( - 3 ) ] ^ { 2 } + [ ( 0 - 1 ) ] ^ { 2 } } = \sqrt { 4 ^ { 2 } + ( - 1 ) ^ { 2 } } = \sqrt { 16 + 1 } = \sqrt { 17 } \text { units. }$

$\mathrm { EF } = \sqrt { [ ( - 1 ) - 1 ] ^ { 2 } + [ ( 2 - 0 ) ] ^ { 2 } } = \sqrt { ( - 2 ) ^ { 2 } + ( 2 ) ^ { 2 } } = \sqrt { 4 + 4 } = \sqrt { 8 } \text { units. }$

$\mathrm { FC } = \sqrt { [ ( - 1 ) - ( - 2 ) ] ^ { 2 } + [ ( 2 - 4 ) ] ^ { 2 } } = \sqrt { 1 ^ { 2 } + ( - 2 ) ^ { 2 } } = \sqrt { 1 + 4 } = \sqrt { 5 } \text { units }$

Thus, Perimeter of the quadrilateral CDEF is

$\begin{array} { l } { = \sqrt { 10 } \text { units. } + \sqrt { 17 } \text { units. } + \sqrt { 8 } \text { units. } \sqrt { 5 } \text { units. } } \\\\ { = ( \sqrt { 10 } + \sqrt { 17 } + \sqrt { 8 } + \sqrt { 5 } ) \text { units. } } \end{array}$

Hence, the perimeter of the quadrilateral CDEF is $( \sqrt { 10 } + \sqrt { 17 } + \sqrt { 8 } + \sqrt { 5 } )$ units.