# 6.3 Geometry  (Page 5/7)

 Page 5 / 7
$\begin{array}{ccc}\hfill PS& =& \sqrt{{\left({x}_{1}-{x}_{2}\right)}^{2}+{\left({y}_{1}-{y}_{2}\right)}^{2}}\hfill \\ & =& \sqrt{{\left(0-2\right)}^{2}+{\left(-0.5-1\right)}^{2}}\hfill \\ & =& \sqrt{{\left(-2\right)}^{2}+{\left(-1.5\right)}^{2}}\hfill \\ & =& \sqrt{4+2.25}\hfill \\ & =& \sqrt{6.25}\hfill \end{array}$

and

$\begin{array}{ccc}\hfill QS& =& \sqrt{{\left({x}_{1}-{x}_{2}\right)}^{2}+{\left({y}_{1}-{y}_{2}\right)}^{2}}\hfill \\ & =& \sqrt{{\left(0-\left(-2\right)\right)}^{2}+{\left(-0.5-\left(-2\right)\right)}^{2}}\hfill \\ & =& \sqrt{{\left(0+2\right)\right)}^{2}{+\left(-0.5+2\right)\right)}^{2}}\hfill \\ & =& \sqrt{{\left(2\right)\right)}^{2}{+\left(-1.5\right)\right)}^{2}}\hfill \\ & =& \sqrt{4+2.25}\hfill \\ & =& \sqrt{6.25}\hfill \end{array}$

It can be seen that $PS=QS$ as expected.

The following video provides a summary of the midpoint of a line.

## Co-ordinate geometry

1. In the diagram given the vertices of a quadrilateral are F(2;0), G(1;5), H(3;7) and I(7;2).
1. What are the lengths of the opposite sides of FGHI?
2. Are the opposite sides of FGHI parallel?
3. Do the diagonals of FGHI bisect each other?
2. A quadrialteral ABCD with vertices A(3;2), B(1;7), C(4;5) and D(1;3) is given.
2. Find the lengths of the sides of the quadrilateral.
3. ABCD is a quadrilateral with verticies A(0;3), B(4;3), C(5;-1) and D(-1;-1).
1. Show that:
2. AB $\parallel$ DC
2. What name would you give to ABCD?
3. Show that the diagonals AC and BD do not bisect each other.
4. P, Q, R and S are the points (-2;0), (2;3), (5;3), (-3;-3) respectively.
1. Show that:
1. SR = 2PQ
2. SR $\parallel$ PQ
2. Calculate:
1. PS
2. QR
5. EFGH is a parallelogram with verticies E(-1;2), F(-2;-1) and G(2;0). Find the co-ordinates of H by using the fact that the diagonals of a parallelogram bisect each other.

## Transformations

In this section you will learn about how the co-ordinates of a point change when the point is moved horizontally and vertically on the Cartesian plane. You will also learn about what happens to the co-ordinates of a point when it is reflected on the $x$ -axis, $y$ -axis and the line $y=x$ .

## Translation of a point

When something is moved in a straight line, we say that it is translated . What happens to the co-ordinates of a point that is translated horizontally or vertically?

## Discussion : translation of a point vertically

Complete the table, by filling in the co-ordinates of the points shown in the figure.

 Point $x$ co-ordinate $y$ co-ordinate A B C D E F G

What do you notice about the $x$ co-ordinates? What do you notice about the $y$ co-ordinates? What would happen to the co-ordinates of point A, if it was moved to the position of point G?

When a point is moved vertically up or down on the Cartesian plane, the $x$ co-ordinate of the point remains the same, but the $y$ co-ordinate changes by the amount that the point was moved up or down.

For example, in [link] Point A is moved 4 units upwards to the position marked by G. The new $x$ co-ordinate of point A is the same ( $x$ =1), but the new $y$ co-ordinate is shifted in the positive $y$ direction 4 units and becomes $y$ =-2 +4 =2. The new co-ordinates of point A are therefore G(1;2). Similarly, for point B that is moved downwards by 5 units, the $x$ co-ordinate is the same ( $x=-2,5$ ), but the $y$ co-ordinate is shifted in the negative $y$ -direction by 5 units. The new $y$ co-ordinate is therefore $y$ =2,5 -5 =-2,5. Point A is moved 4 units upwards to the position marked by G. Point B is moved 5 units downwards to the position marked by H.

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers! By OpenStax By Rhodes By OpenStax By Janet Forrester By Candice Butts By OpenStax By Rhodes By Yasser Ibrahim By Zarina Chocolate By Robert Morris