Question

question
find the distance between the two points in simplest radical form.
answer attempt 1 out of 2
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Explanation:

1. First, assume the two - point formula:

• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let's assume the two points from the graph are \((x_1,y_1)\) and \((x_2,y_2)\). Suppose the first point has coordinates \((0, - 1)\) and the second point has coordinates \((0,5)\).

1. Then, substitute the values into the formula:

• Here, \(x_1 = 0\), \(y_1=-1\), \(x_2 = 0\), \(y_2 = 5\).
• \(d=\sqrt{(0 - 0)^2+(5-( - 1))^2}\).
• First, calculate the values inside the square - root: \((0 - 0)^2=0\) and \(5-( - 1)=5 + 1 = 6\), so \((5-( - 1))^2=6^2 = 36\).
• Then \(d=\sqrt{0 + 36}=\sqrt{36}=6\).

If we assume the points are \((x_1,y_1)\) and \((x_2,y_2)\) in a general sense and calculate step - by - step:

Step1: Identify the coordinates

Let the two points be \((x_1,y_1)\) and \((x_2,y_2)\). From the graph (assuming we can read the coordinates), say \((x_1,y_1)=(0,-1)\) and \((x_2,y_2)=(0,5)\).

Step2: Apply the distance formula

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substitute \(x_1 = 0\), \(y_1=-1\), \(x_2 = 0\), \(y_2 = 5\) into it. We get \(d=\sqrt{(0 - 0)^2+(5-( - 1))^2}=\sqrt{0+(5 + 1)^2}=\sqrt{6^2}\).

Step3: Simplify the result

\(\sqrt{6^2}=6\).

Answer:

\(6\)