Calculate the distance between the following points:F(-9, -14) and G(1,-19)Write your answer in simplest radical form.

To calculate the distance between two points in a plane, we can use the distance formula derived from the Pythagorean theorem, which is:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

Here, F(-9, -14) and G(1,-19) are the two points. So, x1 = -9, y1 = -14, x2 = 1, and y2 = -19.

Substitute these values into the formula:

d = sqrt[(1 - (-9))² + ((-19) - (-14))²] d = sqrt[(1 + 9)² + ((-19 + 14))²] d = sqrt[(10)² + (-5)²] d = sqrt[(100) + (25)] d = sqrt[125]

So, the distance between points F and G is sqrt[125].

However, this is not in simplest radical form. To simplify, we find the prime factorization of 125, which is 555. We group them into pairs, and each pair can come out of the square root as its own number.

So, sqrt[125] = sqrt[555] = 5sqrt[5].

Therefore, the distance between points F and G in simplest radical form is 5sqrt[5].