QuestionCalculate the distance between the points $(-6,-5)$ and $(2,0)$ .

Studdy Solution

STEP 1

Assumptions1. The two points are given as $(-6,-5)$ and $(,0)$ . We are working in a-dimensional Cartesian coordinate system

STEP 2

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a2-dimensional Cartesian coordinate system can be found using the distance formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, we can plug in the given values for the points into the distance formula.
$d = \sqrt{(2 - (-6))^2 + (0 - (-5))^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(2 +6)^2 + (0 +)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{8^2 +5^2}$

STEP 6

implify further.
$d = \sqrt{64 +25}$

STEP 7

Add the two numbers under the square root.
$d = \sqrt{89}$ The distance between the points $(-6,-5)$ and $(2,0)$ is $\sqrt{89}$ units.

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QuestionCalculate the distance between the points $(-6,-5)$ and $(2,0)$ .

Studdy Solution

STEP 1

Assumptions1. The two points are given as $(-6,-5)$ and $(,0)$ . We are working in a-dimensional Cartesian coordinate system

STEP 2

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a2-dimensional Cartesian coordinate system can be found using the distance formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, we can plug in the given values for the points into the distance formula.
$d = \sqrt{(2 - (-6))^2 + (0 - (-5))^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(2 +6)^2 + (0 +)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{8^2 +5^2}$

STEP 6

implify further.
$d = \sqrt{64 +25}$

STEP 7

Add the two numbers under the square root.
$d = \sqrt{89}$ The distance between the points $(-6,-5)$ and $(2,0)$ is $\sqrt{89}$ units.

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QuestionCalculate the distance between the points (−6,−5)(-6,-5)(−6,−5) and (2,0)(2,0)(2,0).

Studdy Solution

STEP 1

Assumptions1. The two points are given as (−6,−5)(-6,-5)(−6,−5) and (,0)(,0)(,0). We are working in a-dimensional Cartesian coordinate system

STEP 2

The distance between two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a2-dimensional Cartesian coordinate system can be found using the distance formulad=(x2−x1)2+(y2−y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}d=(x2−x1)2+(y2−y1)2​

STEP 3

Now, we can plug in the given values for the points into the distance formula.d=(2−(−6))2+(0−(−5))2d = \sqrt{(2 - (-6))^2 + (0 - (-5))^2}d=(2−(−6))2+(0−(−5))2​

STEP 4

implify the expression inside the square root.d=(2+6)2+(0+)2d = \sqrt{(2 +6)^2 + (0 +)^2}d=(2+6)2+(0+)2​

STEP 5

Calculate the squares.d=82+52d = \sqrt{8^2 +5^2}d=82+52​

STEP 6

implify further.d=64+25d = \sqrt{64 +25}d=64+25​

STEP 7

Add the two numbers under the square root.d=89d = \sqrt{89}d=89​The distance between the points (−6,−5)(-6,-5)(−6,−5) and (2,0)(2,0)(2,0) is 89\sqrt{89}89​ units.

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QuestionCalculate the distance between the points $(-6,-5)$ and $(2,0)$ .

Assumptions1. The two points are given as $(-6,-5)$ and $(,0)$ . We are working in a-dimensional Cartesian coordinate system

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a2-dimensional Cartesian coordinate system can be found using the distance formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, we can plug in the given values for the points into the distance formula.
$d = \sqrt{(2 - (-6))^2 + (0 - (-5))^2}$

implify the expression inside the square root.
$d = \sqrt{(2 +6)^2 + (0 +)^2}$

Calculate the squares.
$d = \sqrt{8^2 +5^2}$

implify further.
$d = \sqrt{64 +25}$

Add the two numbers under the square root.
$d = \sqrt{89}$ The distance between the points $(-6,-5)$ and $(2,0)$ is $\sqrt{89}$ units.