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. (1,4)(-6,4)

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Presentation transcript:

Let's find the distance between two points. So the distance from (-6,4) to (1,4) is 7. (1,4)(-6,4) 7 units apart

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. (-6,-3)(-6,4) 7 units apart

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) 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.

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 d gives us: Let's start by finding the distance from (x 1,y 1 ) to (x2,y2)(x2,y2) d 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

Let's use it to find the distance between (3, -5) and (-1,4) (x1,y1)(x1,y1)(x2,y2)(x2,y2) found with a calculator Plug these values in the distance formula

Example 2 Determine if triangle ABC with vertices A(-3,4), B(5,2) and C(-1,-5) is an isosceles triangle. (Hint: An isosceles triangle must have at least 2 sides of equal length.) A(-3,4) B(5,2) C(-1,-5)

A(-3,4) B(5,2) C(-1,-5) BC and AC have the same length so triangle ABC is Isosceles.

Zayed althani school Math department Mohamad badawi : Find the area of the circle in the figure أوجد مساحة الدائرة في الشكل Worksheet ( 1 ) The Distance Formula Hint : find r using the distance formula Remember that :

Zayed althani school Math department Mohamad badawi : Draw and shade triangle ABC where : A ( -1, 3 ), B ( -2, -1 ), C ( 3, 2 ) then prove that the triangle is isosceles. ارسم وظلل المثلث الذي رؤوسه ثم برهن انه متساوي الساقين Worksheet ( 2 ) A ( -1, 3 ), B ( -2, -1 ), C ( 3, 2 ) The Distance Formula