Question

Use the coordinate plane to estimate the distance between the two points. Then use the distance formula to find the distance between the points. Round the result to the nearest hundredth. \((1,5),(-3,1)\) (GRAPH CAN'T COPY)

Short answer

The distance between the points \(A(1,5)\) and \(B(-3,1)\) is 5.66 units.

Step-by-step solution

Identify the Coordinates

The two points given in this problem are \(A(1,5)\) and \(B(-3,1)\). Therefore, \(A(x1,y1)\) and \(B(x2,y2)\). Specifically, \(x1 = 1, y1 = 5, x2 = -3\), and \(y2 = 1\).

Apply the Distance Formula

Substitute the coordinates of each point into the distance formula \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\). This gives: \(\sqrt{(-3 - 1)^2 + (1 - 5)^2}\), which simplifies to: \(\sqrt{(-4)^2 + (-4)^2} = \sqrt{16 + 16}\).

Calculate the Distance

Continuing with the calculation, we get \(\sqrt{32}\).

Round the Result

Converting \(\sqrt{32}\) into a decimal gives approximately 5.66. Rounding this to the nearest hundredth results in 5.66.