Question

find the distance between the two points in simplest radical form.

Explanation:

1. Explanation:

• First, assume the two - point formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). But since the points are not given explicitly, let's assume the points are \((x_1,y_1)\) and \((x_2,y_2)\) from the graph. If we assume one point is \((0,5)\) and the other is \(( - 1,-1)\) (assuming the grid - based positions).
• Step 1: Identify the coordinates and find the differences
• Let \((x_1,y_1)=( - 1,-1)\) and \((x_2,y_2)=(0,5)\). Calculate \(x_2 - x_1\) and \(y_2 - y_1\).
• \(x_2 - x_1=0-( - 1)=1\).
• \(y_2 - y_1=5-( - 1)=6\).
• Step 2: Apply the distance formula
• Substitute the values into the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• \(d=\sqrt{(1)^2+(6)^2}=\sqrt{1 + 36}=\sqrt{37}\).

1. Answer:

\(\sqrt{37}\)

Answer:

1. Explanation:

• First, assume the two - point formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). But since the points are not given explicitly, let's assume the points are \((x_1,y_1)\) and \((x_2,y_2)\) from the graph. If we assume one point is \((0,5)\) and the other is \(( - 1,-1)\) (assuming the grid - based positions).
• Step 1: Identify the coordinates and find the differences
• Let \((x_1,y_1)=( - 1,-1)\) and \((x_2,y_2)=(0,5)\). Calculate \(x_2 - x_1\) and \(y_2 - y_1\).
• \(x_2 - x_1=0-( - 1)=1\).
• \(y_2 - y_1=5-( - 1)=6\).
• Step 2: Apply the distance formula
• Substitute the values into the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• \(d=\sqrt{(1)^2+(6)^2}=\sqrt{1 + 36}=\sqrt{37}\).

1. Answer:

\(\sqrt{37}\)