Question

Find the distance between the two points (x, y) = (-7, 2) and (x, y) = (1, -5). Simplify your answer and write the exact answer in simplest radical form for irrational answers.

Answer 1

The distance between the two points (-7, 2) and (1, -5) is the square root of 113 (√113), which is an irrational number in simplest radical form.

Step-by-step explanation:

To find the distance between two points in a coordinate plane, you use the distance formula, which is derived from the Pythagorean theorem. The distance (d) between two points (x1, y1) and (x2, y2) is given by the formula:
d = √((x2 - x1)² + (y2 - y1)²)

For the points (-7, 2) and (1, -5), we substitute these values into the formula:
d = √((1 - (-7))² + (-5 - 2)²)
d = √((1 + 7)² + (-7)²)
d = √(8² + (-7)²)
d = √(64 + 49)
d = √113

So, the distance between the two points is √113, which is an irrational number in simplest radical form since 113 cannot be simplified further.