Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (4, -1) and (-6, 3)

Guida verificata passo dopo passo

Identify the coordinates of the two points: Point 1 is (4, -1) and Point 2 is (-6, 3).

Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Substitute the given coordinates into the formula: \[d = \sqrt{(-6 - 4)^2 + (3 - (-1))^2}\]

Simplify inside the parentheses: \[d = \sqrt{(-10)^2 + (4)^2}\]

Calculate the squares and express the distance in simplified radical form: \[d = \sqrt{100 + 16} = \sqrt{116}\]. Then, simplify the radical if possible before rounding to two decimal places.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Distance Formula

The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and is given by the square root of the sum of the squares of the differences in x-coordinates and y-coordinates: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Video consigliato:

06:36

Solving Quadratic Equations Using The Quadratic Formula

Simplified Radical Form

Simplified radical form means expressing a square root in its simplest form by factoring out perfect squares. This makes the expression easier to interpret and use in further calculations, such as \( \sqrt{50} = 5\sqrt{2} \).

Video consigliato:

5:48

Adding & Subtracting Unlike Radicals by Simplifying

Rounding to Decimal Places

Rounding involves approximating a number to a specified number of decimal places for clarity or practical use. Here, after simplifying the radical, the distance should be rounded to two decimal places, ensuring the answer is both precise and easy to read.

Video consigliato: