QuestionGraph a right triangle with hypotenuse points $(8,7)$ and $(6,3)$ . Find the distance between these points in simplest radical form.

Studdy Solution

STEP 1

Assumptions1. The two given points (8,7) and (6,3) form the hypotenuse of the right triangle. . We are asked to find the distance between these two points, which is the length of the hypotenuse.
3. The distance between two points in a plane is given by the distance formula derived from the Pythagorean theorem.

STEP 2

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

STEP 3

Now, plug in the given values for the points to calculate the distance.
$d = \sqrt{(6 -8)^2 + (3 -7)^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(-2)^2 + (-4)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{4 +16}$

STEP 6

Add the numbers under the square root.
$d = \sqrt{20}$

STEP 7

The number20 can be factored into4 and5, where4 is a perfect square. So, we can simplify the radical.
$d = \sqrt{4 \times5}$

STEP 8

Take the square root of the perfect square (4) out of the square root.
$d =2\sqrt{5}$ The distance between the two points (8,7) and (6,3) is $2\sqrt{5}$ units.

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QuestionGraph a right triangle with hypotenuse points $(8,7)$ and $(6,3)$ . Find the distance between these points in simplest radical form.

Studdy Solution

STEP 1

STEP 2

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

STEP 3

Now, plug in the given values for the points to calculate the distance.
$d = \sqrt{(6 -8)^2 + (3 -7)^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(-2)^2 + (-4)^2}$

STEP 5

Calculate the squares.
$d = \sqrt{4 +16}$

STEP 6

Add the numbers under the square root.
$d = \sqrt{20}$

STEP 7

The number20 can be factored into4 and5, where4 is a perfect square. So, we can simplify the radical.
$d = \sqrt{4 \times5}$

STEP 8

Take the square root of the perfect square (4) out of the square root.
$d =2\sqrt{5}$ The distance between the two points (8,7) and (6,3) is $2\sqrt{5}$ units.

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QuestionGraph a right triangle with hypotenuse points (8,7)(8,7)(8,7) and (6,3)(6,3)(6,3). Find the distance between these points in simplest radical form.

Studdy Solution

STEP 1

STEP 2

The distance between two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a plane is given by the formulad=(x2−x1)2+(y2−y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}d=(x2−x1)2+(y2−y1)2​

STEP 3

Now, plug in the given values for the points to calculate the distance.d=(6−8)2+(3−7)2d = \sqrt{(6 -8)^2 + (3 -7)^2}d=(6−8)2+(3−7)2​

STEP 4

implify the expression inside the square root.d=(−2)2+(−4)2d = \sqrt{(-2)^2 + (-4)^2}d=(−2)2+(−4)2​

STEP 5

Calculate the squares.d=4+16d = \sqrt{4 +16}d=4+16​

STEP 6

Add the numbers under the square root.d=20d = \sqrt{20}d=20​

STEP 7

The number20 can be factored into4 and5, where4 is a perfect square. So, we can simplify the radical.d=4×5d = \sqrt{4 \times5}d=4×5​

STEP 8

Take the square root of the perfect square (4) out of the square root.d=25d =2\sqrt{5}d=25​The distance between the two points (8,7) and (6,3) is 252\sqrt{5}25​ units.

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QuestionGraph a right triangle with hypotenuse points $(8,7)$ and $(6,3)$ . Find the distance between these points in simplest radical form.

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

Now, plug in the given values for the points to calculate the distance.
$d = \sqrt{(6 -8)^2 + (3 -7)^2}$

implify the expression inside the square root.
$d = \sqrt{(-2)^2 + (-4)^2}$

Calculate the squares.
$d = \sqrt{4 +16}$

Add the numbers under the square root.
$d = \sqrt{20}$

The number20 can be factored into4 and5, where4 is a perfect square. So, we can simplify the radical.
$d = \sqrt{4 \times5}$

Take the square root of the perfect square (4) out of the square root.
$d =2\sqrt{5}$ The distance between the two points (8,7) and (6,3) is $2\sqrt{5}$ units.