Question

Find the distance between the points (-3, 4) and (0, -2).

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([0 - (-3)]^2 + [-2 - 4]^2)\implies d=√((0+3)^2+(-6)^2) \\\\\\ d=√(45)\implies d=√(3^2\cdot 5)\implies d=3√(5)`

Answer 2

(

0

,

−

2

)

,

(

4

,

2

)

Use the distance formula to determine the distance between the two points.

Distance

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Substitute the actual values of the points into the distance formula.

√

(

4

−

0

)

2

+

(

2

−

(

−

2

)

)

2

Simplify.

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4

√

2

The result can be shown in multiple forms.

Exact Form:

4

√

2

Decimal Form:

5.65685424

…

Explanation:

hope it helps!