Find the distance between the points (1, 4) and (13, 9).

1. The distance formula squares the horizontal gap, squares the vertical gap, adds them and takes the square root. 2. The horizontal gap is 13 minus 1, which is 12. 3. The vertical gap is 9 minus 4, which is 5. 4. Squaring gives 144 and 25. 5. Adding those gives 169. 6. The square root of 169 is 13, so the distance is 13 units. 7. Seventeen units comes from adding the two gaps instead of using the formula. 8. Twelve units reports only the horizontal gap and ignores the vertical one. 9. Five units reports only the vertical gap. _Source: OpenStax College Algebra (CC BY 4.0), section 2.1 The Rectangular Coordinate Systems and Graphs_