Respuesta :

disatnce bewteen (x1,y1) and (x2,y2) is
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]


so disatnce between (-4,6) and (3,-7) is
[tex]D=\sqrt{(-4-3)^2+(6-(-7))^2}[/tex]
[tex]D=\sqrt{(-7)^2+(6+7)^2}[/tex]
[tex]D=\sqrt{49+(13)^2}[/tex]
[tex]D=\sqrt{49+169}[/tex]
[tex]D=\sqrt{218}[/tex]

the disatnce is √218 units or aprox 14.7648 units

By the distance formula,

[tex]d = \sqrt{( x_2 - x_1) {}^{2} + (y_2 - y_1 {)}^{2} }[/tex]

Here,

[tex]x_1 = -4[/tex]

[tex]y_1 = 6[/tex]

[tex]x_2 = -7[/tex]

[tex]y_2 = 3[/tex]

Hence,

[tex]d = \sqrt{( {(-7 )+(- 4))}^{2} + {( 3 + 6)}^{2} } [/tex]

[tex]d = \sqrt{ {(-11)}^{2} + {9}^{2} } [/tex]

[tex]d = \sqrt{121+ 81} [/tex]

[tex]d = \sqrt{202} [/tex]