The Distance Formula

Finding The Distance Between PointsOn maps and other grids, you often need to find the distance between two points not on the same grid line.This is used for:Taking a car tripFlying a planeTargeting a rocketComputing the distance a football is thrown

Investigating Distance

Plot A (0,0) and B (4,5) on graph paper. Then draw a right triangle that has the line segment AB as its hypotenuse.Label the coordinates of the vertices.Find the length of the legs of the right triangle.Use the Pythagorean Theorem to find the length of the hypotenuse.

complete the sample problem in your INB

Complete the next two on your own

Steps to finding distance on the coordinate grid using the Pythagorean Theorem

Graph the points on the coordinate plane, if needed Draw a right triangle, with the hypotenuse connecting the two points. Count vertically for the 1st leg length Count horizontally for the 2nd leg length. Use the Pythagorean Theorem to find the hypotenuse and therefore the distance between the two points.

Assignment for Today Complete worksheet on finding distance between two points using the Pythagorean Theorem

Review of finding distance on the coordinate plane

Finding distance on the coordinate plane

Without directly using the Pythagorean Formula

Finding distance on a map Find the distance from the corner of Avenue 2 and 1st Street (A) to the corner of Avenue 4 and 6th Street.

Steps for finding distance

Your turn

Steps to solving for distance

Example 1 Find the distance between the points

A (3, 7) and B (8, 2)

Example 2 Find the distance between the points (3,-6) and

(-9,0)

Example 3 Find the distance between the two points

(8,-8) and the origin

Assignment Complete the worksheet

Applications of Distance Formula

USING THE PYTHAGOREAN THEOREM

NASA MAP

USING THE DISTANCE FORMULANASA MAP

Another example If a building is located on a city map at (2,6) and the park is located at (2,0). Find the distance between the building and the park.

Final Example On the galactic grid, a quasar is located at (54, 29). A black hole is located at (32, 15). How far is the quasar from the black hole.

DISTANCE FORMULA

WHAT DID WE LEARN?HOW TO COMPUTE DISTANCE USING THE PYTHAGOREAN THEOREM AND THE DISTANCE FORMULAHow to find distances from a map

THE END