Pergunta

1)) Find the distance between the points (-10,-8) and (0,-2) 4) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units
Solução

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BrunoMestre · Tutor por 5 anos
Responder
The distance between the points \((-10,-8)\) and \((0,-2)\) is \(2\sqrt{34}\) units.
Explicação
## Step 1<br />The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane can be calculated using the distance formula. The distance formula is derived from the Pythagorean theorem and is given as:<br />### \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)<br /><br />## Step 2<br />In this problem, the two points are \((-10,-8)\) and \((0,-2)\). So, \(x_1 = -10\), \(y_1 = -8\), \(x_2 = 0\), and \(y_2 = -2\).<br /><br />## Step 3<br />Substitute these values into the distance formula:<br />### \(d = \sqrt{(0 - (-10))^2 + ((-2) - (-8))^2}\)<br /><br />## Step 4<br />Simplify the expression inside the square root:<br />### \(d = \sqrt{(10)^2 + (6)^2}\)<br /><br />## Step 5<br />Calculate the squares and add them:<br />### \(d = \sqrt{100 + 36}\)<br /><br />## Step 6<br />Add the results:<br />### \(d = \sqrt{136}\)<br /><br />## Step 7<br />Simplify the square root:<br />### \(d = 2\sqrt{34}\)
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