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The coordinates of the point
E are
(1,4) and the coordinates of point
F are
(1,-5). What is the distance, in units, between the point
E and point
F ?
Answer: units

The coordinates of the point $E$ are $(1,4)$ and the coordinates of point $F$ are $(1,-5)$ . What is the distance, in units, between the point $E$ and point $F$ ? $\newline$ Answer: $\square$ units

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Find the magnitude of a three-dimensional vector

Full solution

Q. The coordinates of the point

E

are

(1,4)

and the coordinates of point

F

are

(1,-5)

. What is the distance, in units, between the point

E

and point

F

?

\newline

Answer:

\square

units

Use Distance Formula: To find the distance between two points in a $2$ D coordinate system, we use the distance formula which is derived from the Pythagorean theorem. The distance formula is: $\newline$ Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ $\newline$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
Substitute Coordinates: Substitute the coordinates of points E and F into the distance formula. $\newline$ Point E has coordinates $(1,4)$ and point F has coordinates $(1,-5)$ . $\newline$ Distance $= \sqrt{(1 - 1)^2 + (-5 - 4)^2}$
Simplify Expression: Simplify the expression inside the square root. $\newline$ Distance = $\sqrt{(0)^2 + (-9)^2}$ $\newline$ Distance = $\sqrt{0 + 81}$
Calculate Square Root: Calculate the square root to find the distance. $\newline$ Distance = $\sqrt{81}$ $\newline$ Distance = $9$

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