Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary). \[ (8,-5) \text { and }(3,-3) \]

To graph the right triangle formed by the points \((8, -5)\) and \((3, -3)\), we first need to find the distance between these two points, which will be the length of the hypotenuse of the triangle. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a Cartesian plane can be calculated using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates of the points \((8, -5)\) and \((3, -3)\): - \(x_1 = 8\), \(y_1 = -5\) - \(x_2 = 3\), \(y_2 = -3\) Now, we can calculate the differences: \[ x_2 - x_1 = 3 - 8 = -5 \] \[ y_2 - y_1 = -3 - (-5) = -3 + 5 = 2 \] Now, we can substitute these values into the distance formula: \[ d = \sqrt{(-5)^2 + (2)^2} \] \[ d = \sqrt{25 + 4} \] \[ d = \sqrt{29} \] Now, we can approximate \(\sqrt{29}\): \[ \sqrt{29} \approx 5.385 \] Rounding to the nearest tenth, we get: \[ d \approx 5.4 \] ### Summary - The distance between the points \((8, -5)\) and \((3, -3)\) is approximately **5.4** units. ### Graphing the Triangle To graph the right triangle, we can plot the points \((8, -5)\) and \((3, -3)\) on a coordinate plane. The right triangle can be formed by drawing vertical and horizontal lines from each point to meet at a right angle. 1. Plot the point \((8, -5)\). 2. Plot the point \((3, -3)\). 3. Draw a vertical line from \((3, -3)\) to \((3, -5)\). 4. Draw a horizontal line from \((3, -5)\) to \((8, -5)\). This will create a right triangle with the hypotenuse being the line segment connecting \((8, -5)\) and \((3, -3)\).