Question

find the distance of ab *simplify the radical

Explanation:

1. Assume the coordinates of points:

• Let's assume that point \(A=(x_1,y_1)\) and point \(B=(x_2,y_2)\). From the grid - if we count the horizontal and vertical displacements. Suppose \(A\) is at the origin \((0,0)\) and \(B\) is at \((8,6)\) (assuming each grid square is of unit length).
• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Substitute the coordinates into the formula:

• Here, \(x_1 = 0,y_1 = 0,x_2 = 8,y_2 = 6\).
• \(d=\sqrt{(8 - 0)^2+(6 - 0)^2}=\sqrt{8^2+6^2}\).
• First, calculate \(8^2 = 64\) and \(6^2 = 36\). Then \(d=\sqrt{64 + 36}\).
• \(64+36=100\), so \(d=\sqrt{100}\).
• \(\sqrt{100}=10\).

Step1: Identify the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Substitute the coordinates

Substitute \(x_1 = 0,y_1 = 0,x_2 = 8,y_2 = 6\) into the formula: \(d=\sqrt{(8 - 0)^2+(6 - 0)^2}=\sqrt{64 + 36}\).

Step3: Simplify the expression

\(64 + 36=100\), so \(d=\sqrt{100}=10\).

Answer:

10