California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

What is the distance between the points (2, 3) and (5, 7)?

1. 3

2. √(18)

3. √(16)

4. 5

The correct answer is: √(18)

To find the distance between the points (2, 3) and (5, 7), you can use the distance formula, which is derived from the Pythagorean theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] In this case, the coordinates are \((2, 3)\) and \((5, 7)\). Substituting the values into the distance formula: 1. Calculate \(x_2 - x_1\): - \(5 - 2 = 3\) 2. Calculate \(y_2 - y_1\): - \(7 - 3 = 4\) 3. Substitute these values into the formula: - \(d = \sqrt{(3)^2 + (4)^2}\) - \(d = \sqrt{9 + 16}\) 4. Simplifying further: - \(d = \sqrt{25}\) 5