Distance formula.

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Presentation transcript:

Distance formula

Horizontal and vertical distances between points on a coordinate plane can be counted. The Pythagorean Theorem makes it possible to find diagonal distance on a coordinate plane. Let’s explore……

Step one: On a sheet of grid paper, draw a coordinate plane. Step two: Plot the ordered pairs below on the coordinate plane and connect them in the given order. Connect the last point to the first point. A(3 ,7) B(-8, 7) C(-8, -1) D(3, -1) Step three: What is the name of the quadrilateral formed? Step four: Find the length of each side of the quadrilateral. What is the perimeter of the figure?

Step five:. Draw another coordinate plane Step five: Draw another coordinate plane. Plot the points and connect them in the order given. Connect the last point to the first point. X(-3, -2) Y(-3, 4) Z(5,4) Step six: Classify the triangle based on its angles. Step seven: Find the length of the legs of the triangle. Step eight: Use the Pythagorean Theorem to find the length of the hypotenuse of the triangle. Step nine: What is the perimeter of the triangle?

FINDING THE DISTANCE ON THE COORDINATE PLANE You can use the Pythagorean Theorem to find the distance between two points on the coordinate plane. Plot the points on a coordinate plane. Draw in a right triangle. Find the distance between the two points using the Pythagorean Theorem a² + b² = c²

Try these:

Plot the points: A(2, 8) B(2,5) C(6,5) D(8, 10) Find the perimeter of the shape.

Now, take time to complete the practice worksheet. You may work with you your group or with your elbow partner. Homework: complete the worksheet.

You can also use the DISTANCE FORMULA to find the distance between two points on the coordinate plane. You can use the formula: The distance formula is based on the Pythagorean Theorem:

Find the distance between the two points using the distance formula. Now use the Theorem of Pythagoras to check your answer.

Find the area and perimeter of the shape. Show all your work.

On a map, each unit represents 45 miles On a map, each unit represents 45 miles. West Point, New York is located at (1.5, 2) and Annapolis, Maryland is located at (-1.5, -1.5). What is the approximate distance between West Point and Annapolis?

Two cars leave a house in Richmond, Virginia Two cars leave a house in Richmond, Virginia. One of the cars travels 8 miles north and then 6 miles east. The second car travels 12 miles south and then 9 miles west. How far apart are the cars?

Find the perimeter of a square ABCD if two of the vertices are A(1, 3) and B(-2, 1).

Square PQRS has vertices P(-4, 0), Q(0, 4), R(4, 0) and S(0, -4) Square PQRS has vertices P(-4, 0), Q(0, 4), R(4, 0) and S(0, -4). Find the area and perimeter of square PQRS. Leave your answer as a simplified radical.

Now, use your knowledge of the Pythagorean Theorem and the Distance Formula, and complete the practice worksheet. Complete Numbers: 1 – 10 (odds) Complete Problems: 11 – 16 Show all your work. Plot the points on grid paper. You will turn this in for a grade. Homework: complete the worksheet