QuestionGraph a right triangle using points $(7,-7)$ and $(9,-9)$ . Find the distance between them to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The two points given, $(7,-7)$ and $(9,-9)$ , form the hypotenuse of a right triangle. . We need to find the distance between these two points, which is the length of the hypotenuse.
3. The distance is calculated using the Euclidean distance formula.

STEP 2

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the points $(x1, y1)$ and $(x2, y2)$ to calculate the distance.
$Distance = \sqrt{(9 -7)^2 + (-9 - (-7))^2}$

STEP 4

implify the expression inside the square root.
$Distance = \sqrt{(2)^2 + (-2)^2}$

STEP 5

Calculate the squares inside the square root.
$Distance = \sqrt{4 +4}$

STEP 6

Add the numbers inside the square root.
$Distance = \sqrt{8}$

STEP 7

implify the square root.
$Distance =2\sqrt{2}$

STEP 8

If necessary, round the distance to the nearest tenth.
$Distance \approx2.8$ The distance between the two points $(7,-7)$ and $(,-)$ is approximately $2.8$ units.

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QuestionGraph a right triangle using points $(7,-7)$ and $(9,-9)$ . Find the distance between them to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The two points given, $(7,-7)$ and $(9,-9)$ , form the hypotenuse of a right triangle. . We need to find the distance between these two points, which is the length of the hypotenuse.
3. The distance is calculated using the Euclidean distance formula.

STEP 2

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the points $(x1, y1)$ and $(x2, y2)$ to calculate the distance.
$Distance = \sqrt{(9 -7)^2 + (-9 - (-7))^2}$

STEP 4

implify the expression inside the square root.
$Distance = \sqrt{(2)^2 + (-2)^2}$

STEP 5

Calculate the squares inside the square root.
$Distance = \sqrt{4 +4}$

STEP 6

Add the numbers inside the square root.
$Distance = \sqrt{8}$

STEP 7

implify the square root.
$Distance =2\sqrt{2}$

STEP 8

If necessary, round the distance to the nearest tenth.
$Distance \approx2.8$ The distance between the two points $(7,-7)$ and $(,-)$ is approximately $2.8$ units.

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QuestionGraph a right triangle using points (7,−7)(7,-7)(7,−7) and (9,−9)(9,-9)(9,−9). Find the distance between them to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The two points given, (7,−7)(7,-7)(7,−7) and (9,−9)(9,-9)(9,−9), form the hypotenuse of a right triangle. . We need to find the distance between these two points, which is the length of the hypotenuse.3. The distance is calculated using the Euclidean distance formula.

STEP 2

The Euclidean distance between two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a plane is given by the formulaDistance=(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 points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) to calculate the distance.Distance=(9−7)2+(−9−(−7))2Distance = \sqrt{(9 -7)^2 + (-9 - (-7))^2}Distance=(9−7)2+(−9−(−7))2​

STEP 4

implify the expression inside the square root.Distance=(2)2+(−2)2Distance = \sqrt{(2)^2 + (-2)^2}Distance=(2)2+(−2)2​

STEP 5

Calculate the squares inside the square root.Distance=4+4Distance = \sqrt{4 +4}Distance=4+4​

STEP 6

Add the numbers inside the square root.Distance=8Distance = \sqrt{8}Distance=8​

STEP 7

implify the square root.Distance=22Distance =2\sqrt{2}Distance=22​

STEP 8

If necessary, round the distance to the nearest tenth.Distance≈2.8Distance \approx2.8Distance≈2.8The distance between the two points (7,−7)(7,-7)(7,−7) and (,−)(,-)(,−) is approximately 2.82.82.8 units.

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QuestionGraph a right triangle using points $(7,-7)$ and $(9,-9)$ . Find the distance between them to the nearest tenth.

Assumptions1. The two points given, $(7,-7)$ and $(9,-9)$ , form the hypotenuse of a right triangle. . We need to find the distance between these two points, which is the length of the hypotenuse.
3. The distance is calculated using the Euclidean distance formula.

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, plug in the given values for the points $(x1, y1)$ and $(x2, y2)$ to calculate the distance.
$Distance = \sqrt{(9 -7)^2 + (-9 - (-7))^2}$

implify the expression inside the square root.
$Distance = \sqrt{(2)^2 + (-2)^2}$

Calculate the squares inside the square root.
$Distance = \sqrt{4 +4}$

Add the numbers inside the square root.
$Distance = \sqrt{8}$

implify the square root.
$Distance =2\sqrt{2}$

If necessary, round the distance to the nearest tenth.
$Distance \approx2.8$ The distance between the two points $(7,-7)$ and $(,-)$ is approximately $2.8$ units.