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) is (x1, y1) and G(1, -19) is (x2, y2).

So, substituting the given values into the formula, we get:

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]

The simplest radical form of 125 is 5√5 (since 125 = 25*5 and square root of 25 is 5).

So, the distance between points F and G is 5√5 units.

Question

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) is (x1, y1) and G(1, -19) is (x2, y2).

So, substituting the given values into the formula, we get:

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]

The simplest radical form of 125 is 5√5 (since 125 = 25*5 and square root of 25 is 5).

So, the distance between points F and G is 5√5 units.

Knowee AI · Accepted Answer

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) is (x1, y1) and G(1, -19) is (x2, y2).

So, substituting the given values into the formula, we get:

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]

The simplest radical form of 125 is 5√5 (since 125 = 25*5 and square root of 25 is 5).

So, the distance between points F and G is 5√5 units.

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