Final answer:
To find the distance between the two points (1,2) and (3,7), calculate the leg lengths as the differences in the x and y coordinates, which are 2 and 5 respectively. Apply the Pythagorean theorem to get the hypotenuse length as the square root of 29, which is approximately 5.4 units, not 8.6 units.
Step-by-step explanation:
To calculate the distance between two points on a coordinate plane, one can use the Pythagorean theorem. The distance between points (1,2) and (3,7) can be determined by drawing a right triangle where the line segment connecting these points forms the hypotenuse.
The lengths of the legs of the right triangle are actually the differences in the x-coordinates (which is 3 - 1 = 2) and the y-coordinates (which is 7 - 2 = 5), not 2 and 6 as mentioned. According to the Pythagorean theorem, the formula to find the length of the hypotenuse (c) is c = /a² + b².
Substituting the correct leg lengths into the theorem: c = /2² + 5² = /4 + 25 = /29.
The length of the hypotenuse is therefore c = /29 which is approximately 5.4 units, not 8.6 units as stated in the question.
(Note that the original question provided incorrect values for the lengths of the legs of the right triangle; therefore, the correction was necessary for accurate calculation.)