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Find the distance between
P(4,4) and
Q(9,7).
The distance between
P and
Q is
◻.
(Simplify your answer. Type an exact answer using radicals as need

Find the distance between $P(4,4)$ and $Q(9,7)$ . $\newline$ The distance between $P$ and $Q$ is $\square$ . $\newline$ (Simplify your answer. Type an exact answer using radicals as need

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Find the magnitude of a three-dimensional vector

Full solution

Q. Find the distance between

P(4,4)

and

Q(9,7)

.

\newline

The distance between

P

and

Q

is

\square

.

\newline

(Simplify your answer. Type an exact answer using radicals as need

Distance Formula: To find the distance between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ in a $2$ -dimensional space, we use the distance formula which is derived from the Pythagorean theorem: $\newline$ Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .
Substitute Coordinates: Substitute the given coordinates into the distance formula: $\newline$ P $(4,4)$ and Q $(9,7)$ gives us: $\newline$ Distance = $\sqrt{(9 - 4)^2 + (7 - 4)^2}$ .
Calculate Differences: Calculate the differences: $\newline$ egin{math}( $9$ - $4$ ) = $5$ ext{ and }( $7$ - $4$ ) = $3$ . $\newline$ ext{}
Square Differences: Square the differences: $5^2 = 25$ and $3^2 = 9$ .
Add Squares: Add the squares of the differences: $25 + 9 = 34$ .
Find Distance: Take the square root of the sum to find the distance: $\newline$ Distance = $\sqrt{34}$ . $\newline$ Since $34$ is not a perfect square, we leave the answer in radical form.

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