Questions: Find the distance between the points (5,10) and (8,6). Write your answer as a whole number or a fully simplified radical expression. units

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] We will substitute the given points \((5, 10)\) and \((8, 6)\) into this formula and compute the distance.

Given points are \((5, 10)\) and \((8, 6)\).

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substitute \((x_1, y_1) = (5, 10)\) and \((x_2, y_2) = (8, 6)\) into the formula: \[ \text{Distance} = \sqrt{(8 - 5)^2 + (6 - 10)^2} \]

Calculate the differences and square them: \[ \text{Distance} = \sqrt{(3)^2 + (-4)^2} \] \[ \text{Distance} = \sqrt{9 + 16} \] \[ \text{Distance} = \sqrt{25} \]

Final Answer