QuestionCalculate the distance between points $(2,-10)$ and $(13,18)$ . Provide exact and rounded to 1 decimal place.

Studdy Solution

STEP 1

Assumptions1. The points are given in the Cartesian coordinate system. . The first point is $(,-10)$ .
3. The second point is $(13,18)$ .
4. The distance formula in two dimensions is d = \sqrt{(x - x1)^ + (y - y1)^}.

STEP 2

Let's denote the first point as $(x1, y1)$ and the second point as $(x2, y2)$ . We can then substitute these values into the distance formula.
$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Substitute the given values into the formula.
$d = \sqrt{(13 -2)^2 + (18 - (-10))^2}$

STEP 4

implify the expressions inside the square root.
$d = \sqrt{(11)^2 + (28)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{121 +784}$

STEP 6

Add the numbers under the square root.
$d = \sqrt{905}$ This is the exact distance between the points $(2,-10)$ and $(13,18)$ .

STEP 7

To find the distance rounded to1 decimal place, we need to take the square root of905.
$d \approx \sqrt{905} \approx30.1$ The distance between the points $(2,-10)$ and $(13,18)$ rounded to1 decimal place is approximately30.1 units.

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QuestionCalculate the distance between points $(2,-10)$ and $(13,18)$ . Provide exact and rounded to 1 decimal place.

Studdy Solution

STEP 1

Assumptions1. The points are given in the Cartesian coordinate system. . The first point is $(,-10)$ .
3. The second point is $(13,18)$ .
4. The distance formula in two dimensions is d = \sqrt{(x - x1)^ + (y - y1)^}.

STEP 2

Let's denote the first point as $(x1, y1)$ and the second point as $(x2, y2)$ . We can then substitute these values into the distance formula.
$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Substitute the given values into the formula.
$d = \sqrt{(13 -2)^2 + (18 - (-10))^2}$

STEP 4

implify the expressions inside the square root.
$d = \sqrt{(11)^2 + (28)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{121 +784}$

STEP 6

Add the numbers under the square root.
$d = \sqrt{905}$ This is the exact distance between the points $(2,-10)$ and $(13,18)$ .

STEP 7

To find the distance rounded to1 decimal place, we need to take the square root of905.
$d \approx \sqrt{905} \approx30.1$ The distance between the points $(2,-10)$ and $(13,18)$ rounded to1 decimal place is approximately30.1 units.

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QuestionCalculate the distance between points (2,−10)(2,-10)(2,−10) and (13,18)(13,18)(13,18). Provide exact and rounded to 1 decimal place.

Studdy Solution

STEP 1

Assumptions1. The points are given in the Cartesian coordinate system. . The first point is (,−10)(,-10)(,−10).3. The second point is (13,18)(13,18)(13,18).4. The distance formula in two dimensions is d = \sqrt{(x - x1)^ + (y - y1)^}.

STEP 2

Let's denote the first point as (x1,y1)(x1, y1)(x1,y1) and the second point as (x2,y2)(x2, y2)(x2,y2). We can then substitute these values into the distance formula.d=(x2−x1)2+(y2−y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}d=(x2−x1)2+(y2−y1)2​

STEP 3

Substitute the given values into the formula.d=(13−2)2+(18−(−10))2d = \sqrt{(13 -2)^2 + (18 - (-10))^2}d=(13−2)2+(18−(−10))2​

STEP 4

implify the expressions inside the square root.d=(11)2+(28)2d = \sqrt{(11)^2 + (28)^2}d=(11)2+(28)2​

STEP 5

Calculate the squares.d=121+784d = \sqrt{121 +784}d=121+784​

STEP 6

Add the numbers under the square root.d=905d = \sqrt{905}d=905​This is the exact distance between the points (2,−10)(2,-10)(2,−10) and (13,18)(13,18)(13,18).

STEP 7

To find the distance rounded to1 decimal place, we need to take the square root of905.d≈905≈30.1d \approx \sqrt{905} \approx30.1d≈905​≈30.1The distance between the points (2,−10)(2,-10)(2,−10) and (13,18)(13,18)(13,18) rounded to1 decimal place is approximately30.1 units.

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QuestionCalculate the distance between points $(2,-10)$ and $(13,18)$ . Provide exact and rounded to 1 decimal place.

Assumptions1. The points are given in the Cartesian coordinate system. . The first point is $(,-10)$ .
3. The second point is $(13,18)$ .
4. The distance formula in two dimensions is d = \sqrt{(x - x1)^ + (y - y1)^}.

Let's denote the first point as $(x1, y1)$ and the second point as $(x2, y2)$ . We can then substitute these values into the distance formula.
$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Substitute the given values into the formula.
$d = \sqrt{(13 -2)^2 + (18 - (-10))^2}$

implify the expressions inside the square root.
$d = \sqrt{(11)^2 + (28)^2}$

Calculate the squares.
$d = \sqrt{121 +784}$

Add the numbers under the square root.
$d = \sqrt{905}$ This is the exact distance between the points $(2,-10)$ and $(13,18)$ .

To find the distance rounded to1 decimal place, we need to take the square root of905.
$d \approx \sqrt{905} \approx30.1$ The distance between the points $(2,-10)$ and $(13,18)$ rounded to1 decimal place is approximately30.1 units.