Transcript The Distance Formula

The Distance Formula
Finding The Distance Between Points
On 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 trip
Flying a plane
Targeting a rocket
Computing 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 FORMULA
NASA 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 FORMULA
How to find distances from a map
THE END