Find the mid point between 2 points

Topic :- Midpoint of 2 points

The midpoint between two points whose coordinates are known will be found. We will also develop a general formula for determining the coordinates of the midpoint and go through an example.
This math help explains ,how to find the midpoint.

Question:

Find the mid-point between

(2,2)and (6,4)

Answer:-

midpoint formula
to points is

  x1+x2          y1+y2
x= -------- , y = -------
    2              2

So ,Let's say.

 ( 2 , 2)   ( 6 , 4 )
   x1  y1     x2  y2


Then the mid point is

       2+6        2+4
   x= ----- , y= ------
        2          2

        8      6
     = ---  , ----
        2       2

     =  4 , 3

So the mid point is (4,3)

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Determine the Attributes of parabola

An Equation of Parabola helps us to find attributes of parabola, after simplification of any given equation we can calculate vertex, focus, directrix etc of the parabola. Here is one such example.

Topic : Parabola

Parabola is a Geometrical figure with standard form x ² = -4ay

Question : Find the vertex, focus, diretrix, and axis of symmetry of the parabola y²+3x-2y-11=0
Solution :

y²+3x-2y-11=0

subtract 3x and add 11 on both the sides

y²+3x-2y-11=0

- 30 + 11 = - 30 + 11
-----------------------------
y²-2y = - 3x + 11

by completing the square method

y²-2y + 1 = - 3x + 11 + 1

(y - 1)² = - 3x + 12

(y - 1)² = - 3(x - 4)

Now x - 4 = 0 so x = 4

and y - 1 = 0 so y = 1

So vertex is (4,1)

Standard form is given by

(y - k)² = 4p(x - h)

so here 4p = -3

p = - 3/4

Focus = (4 + (-3/4), 1) = (4 - 3/4 , 1) = (13/4, 1)

Directix x = 4 - (-3/4)

x = 4 + 3/4

x = 19/4

Axis of symmetry is

x = 4


Solving number of problems like this will help you to solve even difficult problems quickly, for more assistance contact calculus help or geometry help.