Guided Practice

The Distance Formula is given by the following equation:

The Distance Formula is just based on the Pythagorean Theorem.

Subtract the x-coordinates to get the horizontal leg length, and subtract the y-coordinates to get the vertical leg length. The sum of the squares of these lengths is the square of the hypotenuse, so we take the square root of the hypotenuse to determine the distance.

Look at the right triangle on the coordinate plane at the end of the video. Enter a number or addition expression below.

The horizontal distance, a, between points A and B is 9 units, and the vertical distance, b, between points A and B is 18 units.

So, the distance AB is equal to √, or approximately 20.13, units.

Suppose the coordinates of point B are (x_{1}, y_{1}) and the coordinates of point A are (x_{2}, y_{2}).

Then, the horizontal distance between points A and B is |_{1} – _{2}|.

And the vertical distance between points A

and B is |_{1} – _{2}|.

Notice that in the diagram x_{1} may be less than x_{2}, which would make x_{1} – x_{2} a negative number. The same goes for the y-coordinates.

But this doesn't matter, because (x_{1} – x_{2})^{2}, for example, is the same as (x_{2} – x_{1})^{2}. Show how this is true with some examples:

(2 – 4)^{2} = (4 – 2)^{2} =

(8 – 1)^{2} = (1 – 8)^{2} =

Use the Distance Formula to determine the distance, as a decimal, from point C to point D. Round to the nearest hundredth.

Distance ≈ units

Use the Distance Formula to determine the distance, as a decimal, from point P to point Q. Round to the nearest hundredth.

Distance ≈ units

Use the Distance Formula to determine the distance, as a decimal, from point S to point T. Round to the nearest hundredth.

Distance ≈ units

Use the Distance Formula to determine the distance, as a decimal, from point A to point B. Round to the nearest hundredth.

Distance ≈ units

Use the Distance Formula to determine the distance, as a decimal, from point A to point B. Round to the nearest hundredth.

Distance ≈ units

Use the Distance Formula to determine the distance, as a decimal, from point A to point B. Round to the nearest hundredth.

Distance ≈ units

Distance = units

You can use what you know about the Distance Formula to determine the perimeters and areas of shapes on the coordinate plane. For example:

You can determine the perimeter and area of this square, even though its side lengths are not horizontal or vertical.

Each side length of the square is the same length. Write your answers as decimals to the nearest hundredth.

Each side is about units long.

The square's perimeter is about units.

Its area is about square units.

Determine the approximate perimeter and area of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

Area = square units

Determine the approximate perimeter and area of the trapezoid. Round to the nearest hundredth.

Perimeter ≈ units

Area = square units

Determine the approximate perimeter and area of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

Area = square units

Determine the approximate perimeter and area of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

Area = square units

Determine the approximate perimeter and area of the trapezoid. Round to the nearest hundredth.

Perimeter ≈ units

Area = square units

Determine the approximate perimeter of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

Determine the approximate perimeter of the parallelogram. Round to the nearest hundredth.

Perimeter ≈ units

Triangle ABC has the vertex coordinates A (5, 0), B (8, 4), and C (0, 0). Determine the approximate perimeter of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

Triangle ABC has vertex coordinates A (–4, 4),

B (2, –1), and C (3, 5). Determine the approximate perimeter of the triangle. Round to the nearest hundredth.

Perimeter ≈ units

On a baseball diamond, the distance between each base is 90 feet. Suppose the ball is thrown from exactly halfway between second and third base to first base. What distance was the ball thrown?

Use the questions on the right to determine the distance the ball was thrown.

Write the final distance as a decimal to the nearest hundredth.

The distance between second base and

point D is feet.

The distance between second base and

point E is feet.

So, the approximate distance the ball was

thrown is feet.

Write the distance as a decimal to the nearest hundredth.

The approximate distance between home plate and second base is feet.

Write the distances as decimals to the nearest hundredth.

The approximate distance between point A and point C is units.

The approximate distance between point A and point B is units.

The approximate distance between point A and point D is units.

Write the distances as decimals to the nearest hundredth.

The approximate distance between point B and point C is units.

The approximate distance between point B and point D is units.

Write the distance as a decimal to the nearest hundredth.

The approximate distance between point C and point D is units.