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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 E are (1,4) (1,4) and the coordinates of point F F are (1,−5) (1,-5) . What is the distance, in units, between the point E E and point F F ?\newlineAnswer: □\square units

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Find the magnitude of a three-dimensional vectorright chevron icon

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Q. The coordinates of the point E E are (1,4) (1,4) and the coordinates of point F F are (1,−5) (1,-5) . What is the distance, in units, between the point E E and point F F ?\newlineAnswer: □\square units
  1. Use Distance Formula: To find the distance between two points in a 22D coordinate system, we use the distance formula which is derived from the Pythagorean theorem. The distance formula is:\newlineDistance = (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\newlinewhere (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points.
  2. Substitute Coordinates: Substitute the coordinates of points E and F into the distance formula.\newlinePoint E has coordinates (1,4)(1,4) and point F has coordinates (1,−5)(1,-5).\newlineDistance =(1−1)2+(−5−4)2= \sqrt{(1 - 1)^2 + (-5 - 4)^2}
  3. Simplify Expression: Simplify the expression inside the square root.\newlineDistance = (0)2+(−9)2\sqrt{(0)^2 + (-9)^2}\newlineDistance = 0+81\sqrt{0 + 81}
  4. Calculate Square Root: Calculate the square root to find the distance.\newlineDistance = 81\sqrt{81}\newlineDistance = 99

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