Point E is located at (-2, 2) and point F is located at (4,-6). What is the distance bewtween points E and F?

Mathematics

2 answers:

serious [3.7K]2 years ago

5 0

EF = 10

to calculate the distance use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (4, - 6 )

EF = √(4 + 2 )² + (- 6 - 2 )² = √(36 + 64 ) = √100 = 10

Hoochie [10]2 years ago

4 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{-6})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\d=\sqrt{[4-(-2)]^2+[-6-2]^2}\implies d=\sqrt{(4+2)^2+(-6-2)^2}\\\\\\d=\sqrt{6^2+(-8)^2}\implies d=\sqrt{100}\implies d=10$

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Answer: x = (-3,3), y = (-5,5)

Step-by-step explanation:

Add both of the equations together, for $3x^{2}+3y^{2} = 102$ . Now we can divide both sides by 3, getting $x^2+y^2=34$ . we subtract the first equation from our equation we just got, getting $y^2=25$ y= (5,-5). once we plug that in, we get $50+x^2 = 59$ , $x^2 = 9$ x = (-3,3)