Math / Geometry

QuestionFind the distance between the points $(4,5)$ and $(4,-7)$ .
Distance:

Studdy Solution

STEP 1

1. We are using the Euclidean distance formula to find the distance between two points in a 2-dimensional Cartesian coordinate system.
2. The given points are $(4,5)$ and $(4,-7)$ .

STEP 2

1. Identify the coordinates of the given points.
2. Use the distance formula to calculate the distance between the points.
3. Simplify the expression to find the final distance.

STEP 3

Identify the coordinates of the given points. Let $(x_1, y_1) = (4, 5)$ and $(x_2, y_2) = (4, -7)$ .

STEP 4

Use the distance formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute the given coordinates:
$d = \sqrt{(4 - 4)^2 + (-7 - 5)^2}$

STEP 5

Simplify the expression inside the square root:
$d = \sqrt{0^2 + (-12)^2}$

STEP 6

Simplify further:
$d = \sqrt{0 + 144}$

STEP 7

Evaluate the square root:
$d = \sqrt{144} = 12$
Solution: The distance between the points $(4,5)$ and $(4,-7)$ is $12$ .

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QuestionFind the distance between the points $(4,5)$ and $(4,-7)$ .
Distance:

Studdy Solution

STEP 1

1. We are using the Euclidean distance formula to find the distance between two points in a 2-dimensional Cartesian coordinate system.
2. The given points are $(4,5)$ and $(4,-7)$ .

STEP 2

1. Identify the coordinates of the given points.
2. Use the distance formula to calculate the distance between the points.
3. Simplify the expression to find the final distance.

STEP 3

Identify the coordinates of the given points. Let $(x_1, y_1) = (4, 5)$ and $(x_2, y_2) = (4, -7)$ .

STEP 4

Use the distance formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute the given coordinates:
$d = \sqrt{(4 - 4)^2 + (-7 - 5)^2}$

STEP 5

Simplify the expression inside the square root:
$d = \sqrt{0^2 + (-12)^2}$

STEP 6

Simplify further:
$d = \sqrt{0 + 144}$

STEP 7

Evaluate the square root:
$d = \sqrt{144} = 12$
Solution: The distance between the points $(4,5)$ and $(4,-7)$ is $12$ .

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QuestionFind the distance between the points (4,5)(4,5)(4,5) and (4,−7)(4,-7)(4,−7).Distance:

Studdy Solution

STEP 1

1. We are using the Euclidean distance formula to find the distance between two points in a 2-dimensional Cartesian coordinate system.2. The given points are (4,5)(4,5)(4,5) and (4,−7)(4,-7)(4,−7).

STEP 2

1. Identify the coordinates of the given points.2. Use the distance formula to calculate the distance between the points.3. Simplify the expression to find the final distance.

STEP 3

Identify the coordinates of the given points. Let (x1,y1)=(4,5)(x_1, y_1) = (4, 5)(x1​,y1​)=(4,5) and (x2,y2)=(4,−7)(x_2, y_2) = (4, -7)(x2​,y2​)=(4,−7).

STEP 4

Use the distance 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​Substitute the given coordinates:d=(4−4)2+(−7−5)2d = \sqrt{(4 - 4)^2 + (-7 - 5)^2}d=(4−4)2+(−7−5)2​

STEP 5

Simplify the expression inside the square root:d=02+(−12)2d = \sqrt{0^2 + (-12)^2}d=02+(−12)2​

STEP 6

Simplify further:d=0+144d = \sqrt{0 + 144}d=0+144​

STEP 7

Evaluate the square root:d=144=12d = \sqrt{144} = 12d=144​=12 Solution: The distance between the points (4,5)(4,5)(4,5) and (4,−7)(4,-7)(4,−7) is 121212.

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QuestionFind the distance between the points $(4,5)$ and $(4,-7)$ .
Distance:

1. We are using the Euclidean distance formula to find the distance between two points in a 2-dimensional Cartesian coordinate system.
2. The given points are $(4,5)$ and $(4,-7)$ .

1. Identify the coordinates of the given points.
2. Use the distance formula to calculate the distance between the points.
3. Simplify the expression to find the final distance.

Identify the coordinates of the given points. Let $(x_1, y_1) = (4, 5)$ and $(x_2, y_2) = (4, -7)$ .

Use the distance formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute the given coordinates:
$d = \sqrt{(4 - 4)^2 + (-7 - 5)^2}$

Simplify the expression inside the square root:
$d = \sqrt{0^2 + (-12)^2}$

Simplify further:
$d = \sqrt{0 + 144}$

Evaluate the square root:
$d = \sqrt{144} = 12$
Solution: The distance between the points $(4,5)$ and $(4,-7)$ is $12$ .