Students will be able to: calculate the distance between two
points on a line Slide 2 Slide 3 Question: How do we find the
length of Point A to Point B? B A HINT: What type of triangle is
represented? Slide 4 The formula, derived from the Pythagoras
theorem states that square a and square b, add them together, and
square root them, you get the length of c, hypotenuse. 1.1 Slide 5
2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 Let's find
the distance between two points. So the distance from (-6,4) to
(1,4) is 7. If the points are located horizontally from each other,
the y coordinates will be the same. You can look to see how far
apart the x coordinates are. (1,4)(-6,4) 7 units apart Slide 6
2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 What
coordinate will be the same if the points are located vertically
from each other? So the distance from (-6,4) to (-6,-3) is 7. If
the points are located vertically from each other, the x
coordinates will be the same. You can look to see how far apart the
y coordinates are. (-6,-3)(-6,4) 7 units apart Slide 7
2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 But what
are we going to do if the points are not located either
horizontally or vertically to find the distance between them? Let's
add some lines and make a right triangle. This triangle measures 4
units by 3 units on the sides. If we find the hypotenuse, we'll
have the distance from (0,0) to (4,3). Use slope formula Slope
(m)=change in y-axis (y2-y1) change in x-axis (x2- x1 Let's start
by finding the distance from (0,0) to (4,3) ? 4 3 The Pythagorean
Theorem will help us find the hypotenuse 5 So the distance between
(0,0) and (4,3) is 5 units. Slide 8 2-7-6-5-4-3-21573 0468 7 1 2 3
4 5 6 8 -2 -3 -4 -5 -6 -7 Now let's generalize this method to come
up with a formula so we don't have to make a graph and triangle
every time. Let's add some lines and make a right triangle. Solving
for c gives us: Let's start by finding the distance from (x 1,y 1 )
to (x2,y2)(x2,y2) ? x 2 - x 1 y 2 y 1 Again the Pythagorean Theorem
will help us find the hypotenuse (x 2,y 2 ) (x1,y1)(x1,y1) This is
called the distance formula Slide 9 Let's use it to find the
distance between (3, -5) and (-1,4) (x1,y1)(x1,y1) (x2,y2)(x2,y2) 3
-5 4 CAUTION! You must do the brackets first then powers (square
the numbers) and then add together BEFORE you can square root Don't
forget the order of operations! means approximately equal to found
with a calculator Plug these values in the distance formula Slide
10 First, we square the run, which is x2 x1. Then we square the
rise, which is y2 y1,. We then add these two values together. We
should get this: (x2 x1)squared +( y2 y1)squared As we have seen,
the two values are equal to the hypotenuse squared. Therefore we
have to square root the equation to get the final product: Slide
11
