QuestionCalculate the length of the segment between (2,2) and (5,-3) using the formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first endpoint are (,) . The coordinates of the second endpoint are (5,-3)
3. We are using the Euclidean distance formula to calculate the length of the segment

STEP 2

The Euclidean distance formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$ where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

STEP 3

Now, plug in the given values for the coordinates into the distance formula.
$Distance = \sqrt{(5 -2)^2 + (-3 -2)^2}$

STEP 4

Calculate the differences inside the square roots.
$Distance = \sqrt{(3)^2 + (-)^2}$

STEP 5

Square the differences.
$Distance = \sqrt{9 +25}$

STEP 6

Add the squared differences.
$Distance = \sqrt{34}$ The length of the segment with endpoints at coordinates (2,2) and (5,-3) is $\sqrt{34}$ units.

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QuestionCalculate the length of the segment between (2,2) and (5,-3) using the formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first endpoint are (,) . The coordinates of the second endpoint are (5,-3)
3. We are using the Euclidean distance formula to calculate the length of the segment

STEP 2

The Euclidean distance formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$ where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

STEP 3

Now, plug in the given values for the coordinates into the distance formula.
$Distance = \sqrt{(5 -2)^2 + (-3 -2)^2}$

STEP 4

Calculate the differences inside the square roots.
$Distance = \sqrt{(3)^2 + (-)^2}$

STEP 5

Square the differences.
$Distance = \sqrt{9 +25}$

STEP 6

Add the squared differences.
$Distance = \sqrt{34}$ The length of the segment with endpoints at coordinates (2,2) and (5,-3) is $\sqrt{34}$ units.

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QuestionCalculate the length of the segment between (2,2) and (5,-3) using the formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first endpoint are (,) . The coordinates of the second endpoint are (5,-3)3. We are using the Euclidean distance formula to calculate the length of the segment

STEP 2

The Euclidean distance formula is given byDistance=(x2−x1)2+(y2−y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}Distance=(x2−x1)2+(y2−y1)2​where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

STEP 3

Now, plug in the given values for the coordinates into the distance formula.Distance=(5−2)2+(−3−2)2Distance = \sqrt{(5 -2)^2 + (-3 -2)^2}Distance=(5−2)2+(−3−2)2​

STEP 4

Calculate the differences inside the square roots.Distance=(3)2+(−)2Distance = \sqrt{(3)^2 + (-)^2}Distance=(3)2+(−)2​

STEP 5

Square the differences.Distance=9+25Distance = \sqrt{9 +25}Distance=9+25​

STEP 6

Add the squared differences.Distance=34Distance = \sqrt{34}Distance=34​The length of the segment with endpoints at coordinates (2,2) and (5,-3) is 34\sqrt{34}34​ units.

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QuestionCalculate the length of the segment between (2,2) and (5,-3) using the formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Assumptions1. The coordinates of the first endpoint are (,) . The coordinates of the second endpoint are (5,-3)
3. We are using the Euclidean distance formula to calculate the length of the segment

The Euclidean distance formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$ where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

Now, plug in the given values for the coordinates into the distance formula.
$Distance = \sqrt{(5 -2)^2 + (-3 -2)^2}$

Calculate the differences inside the square roots.
$Distance = \sqrt{(3)^2 + (-)^2}$

Square the differences.
$Distance = \sqrt{9 +25}$

Add the squared differences.
$Distance = \sqrt{34}$ The length of the segment with endpoints at coordinates (2,2) and (5,-3) is $\sqrt{34}$ units.