Questions: Find the distance between the points. (5,4),(4,-1)

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane, we can use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] We will substitute the given points \((5, 4)\) and \((4, -1)\) into this formula and calculate the distance.

We are given two points: \((5, 4)\) and \((4, -1)\).

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substitute the given points into the formula: \[ \text{Distance} = \sqrt{(4 - 5)^2 + (-1 - 4)^2} \]

Calculate the differences and square them: \[ \text{Distance} = \sqrt{(-1)^2 + (-5)^2} \] \[ \text{Distance} = \sqrt{1 + 25} \] \[ \text{Distance} = \sqrt{26} \]

Find the square root of 26: \[ \text{Distance} \approx 5.099 \]

Final Answer