The answer is: " 4.47 units " .
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Explanation:
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Note the Pythagorean theorem for right triangles:
→ a² + b² = c² ;
Solve for the "positive value of "c" ;
in which "c" is the "hypotenuse" ; which is the length of VW ;
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in which one side of a right triangle is from:
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"Point W" {coordinate of "(-4, -2)" to "(-2, -2)" ; which is "2 units" long;
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and another side of the right triangle is from:
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"(-2, -2)" to "(2, 2)" ; which is: "4 units long)
c² = 2² + 4² ;
Solve for the "positive value" of "c" ; which is the "hypotenuse" ; which is the length of VW .
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c² = 4 + 16 = 20 ;
c² = 20 ;
Take the "positive square root" of each side of the equation; to solve for "c" ;
⁺√(c²) = ⁺√20;
to get:
→ c = √4√5 = " 2√5 units " ;
or; using calculator: " √20 = 4.4721359549995794 " ;
→ round to: "4.47 units" .
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