Explain the distance formula. Then use it to calculate the distance between A(1,1) and B(7,-7). Any help please.

you know the Pythagorean Theorem, right?

The hypotenuse is the distance between A and B.

The horizontal distance from A to B is (7-1)
The vertical distance is (-7-1)

Using the Pythagorean theorem, the length of the hypotenuse (the distance AB) is

√((7-1)^2 + (-7-1)^2) = 10

Yes

The distance formula is used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

To use the formula to calculate the distance between A(1,1) and B(7,-7), let's plug in the values:

Distance = √((7 - 1)^2 + (-7 - 1)^2)

Simplifying the equation:

Distance = √((6)^2 + (-8)^2)

Distance = √(36 + 64)

Distance = √(100)

Distance = 10

Therefore, the distance between A(1,1) and B(7,-7) is 10 units.

The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem.

To understand the distance formula, let's consider two points in a two-dimensional plane, A(x1, y1) and B(x2, y2). The distance (d) between these two points can be found using the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Now let's calculate the distance between points A(1, 1) and B(7, -7) using the distance formula:

Step 1: Identify the coordinates of point A and point B.
- Point A: (x1, y1) = (1, 1)
- Point B: (x2, y2) = (7, -7)

Step 2: Substitute the values into the distance formula:

d = √((7 - 1)^2 + (-7 - 1)^2)

Step 3: Simplify the equation:

d = √(6^2 + (-8)^2)
= √(36 + 64)
= √100
= 10

So, the distance between points A(1, 1) and B(7, -7) is 10 units.