Final answer:
The Pythagorean theorem can be used to find the distance between two points on a coordinate plane by substituting the coordinates into the formula and solving for c. For example, using the formula, we can find that the distance between (3, 4) and (7, 2) is 2√5.
Step-by-step explanation:
The Pythagorean theorem can be used to find the distance between two points on a coordinate plane. The formula for the Pythagorean theorem is a² + b² = c², where c represents the hypotenuse of a right triangle, and a and b represent the lengths of the other two sides. In this case, the distance between the two points can be found by substituting the coordinates of the points into the formula and solving for c.
For example, if the two points are (3, 4) and (7, 2), we can calculate the distance as follows:
a = 7 - 3 = 4
b = 2 - 4 = -2
a² + b² = 16 + 4 = 20
c = √20 = 2√5
Therefore, the distance between the two points is 2√5.
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