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](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202501%2F1-find-distance-points-108-024-write-answer-whole-number-thZmZXWzdY0q.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
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
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The distance between the points (-10,-8) and (0,-2) is 2\sqrt{34} units.
Explicação
## Step 1
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:
### d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
## Step 2
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.
## Step 3
Substitute these values into the distance formula:
### d = \sqrt{(0 - (-10))^2 + ((-2) - (-8))^2}
## Step 4
Simplify the expression inside the square root:
### d = \sqrt{(10)^2 + (6)^2}
## Step 5
Calculate the squares and add them:
### d = \sqrt{100 + 36}
## Step 6
Add the results:
### d = \sqrt{136}
## Step 7
Simplify the square root:
### d = 2\sqrt{34}
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:
### d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
## Step 2
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.
## Step 3
Substitute these values into the distance formula:
### d = \sqrt{(0 - (-10))^2 + ((-2) - (-8))^2}
## Step 4
Simplify the expression inside the square root:
### d = \sqrt{(10)^2 + (6)^2}
## Step 5
Calculate the squares and add them:
### d = \sqrt{100 + 36}
## Step 6
Add the results:
### d = \sqrt{136}
## Step 7
Simplify the square root:
### d = 2\sqrt{34}
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