QuestionFind the distance between the points $(1,2)$ and $(4,6)$ using the distance formula.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (1,) . The coordinates of the second point are (4,6)

STEP 2

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane can be calculated using the distance formula derived from the Pythagorean theorem. The formula is $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates of the two points into the distance formula.
$Distance = \sqrt{( -1)^2 + (6 -2)^2}$

STEP 4

Calculate the differences inside the square root.
$Distance = \sqrt{(3)^2 + (4)^2}$

STEP 5

Square the differences inside the square root.
$Distance = \sqrt{9 +16}$

STEP 6

Add the squared differences.
$Distance = \sqrt{25}$

STEP 7

Calculate the square root of25 to find the distance.
$Distance =5$ The distance between the points $(1,2)$ and $(4,6)$ is5 units.

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QuestionFind the distance between the points $(1,2)$ and $(4,6)$ using the distance formula.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (1,) . The coordinates of the second point are (4,6)

STEP 2

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane can be calculated using the distance formula derived from the Pythagorean theorem. The formula is $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates of the two points into the distance formula.
$Distance = \sqrt{( -1)^2 + (6 -2)^2}$

STEP 4

Calculate the differences inside the square root.
$Distance = \sqrt{(3)^2 + (4)^2}$

STEP 5

Square the differences inside the square root.
$Distance = \sqrt{9 +16}$

STEP 6

Add the squared differences.
$Distance = \sqrt{25}$

STEP 7

Calculate the square root of25 to find the distance.
$Distance =5$ The distance between the points $(1,2)$ and $(4,6)$ is5 units.

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QuestionFind the distance between the points (1,2)(1,2)(1,2) and (4,6)(4,6)(4,6) using the distance formula.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (1,) . The coordinates of the second point are (4,6)

STEP 2

The distance between two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a plane can be calculated using the distance formula derived from the Pythagorean theorem. The formula isDistance=(x2−x1)2+(y2−y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}Distance=(x2−x1)2+(y2−y1)2​

STEP 3

Now, plug in the given values for the coordinates of the two points into the distance formula.Distance=(−1)2+(6−2)2Distance = \sqrt{( -1)^2 + (6 -2)^2}Distance=(−1)2+(6−2)2​

STEP 4

Calculate the differences inside the square root.Distance=(3)2+(4)2Distance = \sqrt{(3)^2 + (4)^2}Distance=(3)2+(4)2​

STEP 5

Square the differences inside the square root.Distance=9+16Distance = \sqrt{9 +16}Distance=9+16​

STEP 6

Add the squared differences.Distance=25Distance = \sqrt{25}Distance=25​

STEP 7

Calculate the square root of25 to find the distance.Distance=5Distance =5Distance=5The distance between the points (1,2)(1,2)(1,2) and (4,6)(4,6)(4,6) is5 units.

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QuestionFind the distance between the points $(1,2)$ and $(4,6)$ using the distance formula.

The distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane can be calculated using the distance formula derived from the Pythagorean theorem. The formula is $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, plug in the given values for the coordinates of the two points into the distance formula.
$Distance = \sqrt{( -1)^2 + (6 -2)^2}$

Calculate the differences inside the square root.
$Distance = \sqrt{(3)^2 + (4)^2}$

Square the differences inside the square root.
$Distance = \sqrt{9 +16}$

Add the squared differences.
$Distance = \sqrt{25}$

Calculate the square root of25 to find the distance.
$Distance =5$ The distance between the points $(1,2)$ and $(4,6)$ is5 units.