ADVANCED MATHEMATICS FORM 5 – COORDINATE GEOMETRY – part 1

  -Is the conic section whose eccentricity is equal to zero.
-Coordinate geometry is the study of representation of geometry figure either on two or three dimension under the one of the following steps.

1.      DISTANCE BETWEEN TWO POINTS

-Let’s consider point A and on XY- plane now we need to find the distance from A to B.

Pythagoras theorem

But  

Now,

For case of three of dimension

MID – POINT

–        – A midpoint of line segment, is  the point bisect a line segment.

OR

–        Is the point which divide a certain line into two equal parts.

Proof,

-Consider point A(x₁,y₁), B(x₂,y₂) and R(x,y)

-Consider the figure lie low.

 From, similarities of ΔADR and  ΔRCB.

but,

From equation

 But

  AD=X-X₁

RC=X2-X

For X

For

From equation

But

Then,

 EXAMPLE.

     1.   Find the distance between A and B

    2.     Show that the point and are vertices of isosceles triangle.

    3.      Show that the point and are vertices of  right angled triangles.  

    4.      Show that the point and (0,1) are vertices of square.

Solution.

Given

Since

Then the point A (1,2), B (3,5), C (4,4) are vertices of isosceles triangle.

Hence shown.