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DISTANCE FORMULA
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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……
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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?
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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?
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FINDING THE DISTANCE ON THE COORDINATE PLANEYou can use the Pythagorean Theorem to find the distance between two points on the coordinate plane.
1. Plot the points on a coordinate plane.2. Draw in a right triangle.3. Find the distance between the two points
using the Pythagorean Theorem a² + b² = c²
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Try these:
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Plot the points:
A(2, 8) B(2,5) C(6,5) D(8, 10)
Find the perimeter of the shape.
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Now, take time to complete the practice worksheet.
You may work with you your group or with your elbow partner.
Homework: complete the worksheet.
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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:
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Find the distance between the two points using the distance formula. d =
Now use the Theorem of Pythagoras to check your answer.
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Find the area and perimeter of the shape.
Show all your work.
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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?
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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?
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Find the perimeter of a square ABCD if two of the vertices are A(1, 3) and B(-2, 1).
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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.
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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