For example, find the equation of the tangent to the circle at point
$(1,1)$ . The centre of the circle is at
$(0,0)$ . The equation of the circle is
${x}^{2}+{y}^{2}=2$ .
Any line
$OP$ is drawn (not necessarily in the first quadrant), making an angle of
$\theta $ degrees with the
$x$ -axis. Using the co-ordinates of
$P$ and the angle
$\alpha $ , calculate the co-ordinates of
${P}^{\text{'}}$ , if the line
$OP$ is rotated about the origin through
$\alpha $ degrees.
$P$
$\alpha $
1.
(2, 6)
60
${}^{\circ}$
2.
(4, 2)
30
${}^{\circ}$
3.
(5, -1)
45
${}^{\circ}$
4.
(-3, 2)
120
${}^{\circ}$
5.
(-4, -1)
225
${}^{\circ}$
6.
(2, 5)
-150
${}^{\circ}$
Characteristics of transformations
Rigid transformations like translations, reflections, rotations and glide reflections preserve shape and size, and that enlargement preserves shape but not size.
Geometric transformations:
Draw a large 15
$\times $ 15 grid and plot
$\u25b5ABC$ with
$A(2;6)$ ,
$B(5;6)$ and
$C(5;1)$ . Fill in the lines
$y=x$ and
$y=-x$ .
Complete the table below , by drawing the images of
$\u25b5ABC$ under the given transformations. The first one has been done for you.
A transformation that leaves lengths and angles unchanged is called a rigid transformation. Which of the above transformations are rigid?
Exercises
$\Delta ABC$ undergoes several transformations forming
$\Delta {A}^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}$ . Describe the relationship between the angles and sides of
$\Delta ABC$ and
$\Delta {A}^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}$ (e.g., they are twice as large, the same, etc.)
Transformation
Sides
Angles
Area
Reflect
Reduce by a scale factor of 3
Rotate by 90
${}^{\circ}$
Translate 4 units right
Enlarge by a scale factor of 2
$\Delta DEF$ has
$\widehat{E}={30}^{\circ}$ ,
$DE=4\phantom{\rule{0.166667em}{0ex}}\mathrm{cm}$ ,
$EF=5\phantom{\rule{0.166667em}{0ex}}\mathrm{cm}$ .
$\Delta DEF$ is enlarged by a scale factor of 6 to form
$\Delta {D}^{\text{'}}{E}^{\text{'}}{F}^{\text{'}}$ .
$\Delta XYZ$ has an area of
$6\phantom{\rule{0.166667em}{0ex}}{\mathrm{cm}}^{2}$ . Find the area of
$\Delta {X}^{\text{'}}{Y}^{\text{'}}{Z}^{\text{'}}$ if the points have been transformed as follows:
I would start by learning basic terminology and definitions cause there's a lot of it and learning the different concepts behind psychology and there meanings and there use then go onto introduction into psychology
what we define as science is a systematic arrangement of knowledge based on experimental and observational data.so psychology is a science. as for what kind of science it is depends on how and what information are you using in your approach towards understanding the said data and to what conclusion.
imirror
depending on your approach and understanding Psychology can classify as medical or social science like anthropology
imirror
your friend is under stress because she has not prepared well for the examination what strategies would you suggest her? express in 100 or 150 words
Suppose an individual with OCD experiences obsessive thoughts about germs, contamination, and disease whenever she encounters a doorknob. What might have constituted a viable unconditioned stimulus?
Environment
Heredity(I am not sure about heredity)
Tusita
Helpful. .. thanks
Enos
Sure, anytime
Tusita
I have other questions also
Enos
Based on the factors affecting learning, how do we improve learning
Enos
I think that addressing that everyone learns in their own time
James
Peer group influence can also be another reason
Sorie
Also knowing what's going on at home. what pressure are the parents putting on them.
James
am I close or no
James
also is there a lack of care? going one more step. with peer groups do an activity that shows how much they have in common
James
I think one's society has a big role to play in determining what/when & how he/she learns.
BECHEM
multiple reasons at different stages. at the earliest stages of development in a child is behaviour of people around. A baby starts learning basic social expressions and actions by mimicking the people around it. further social and cultural practices enforces learning and behaviour
imirror
from need to nutrition everything affect development and learning when choosing on a single factor of influence it is necessary to keep these other factors in the mind as environment around people is very plastic and flexible and there are many variables playing active role
imirror
social interaction is surely a big influence hence can be used to improve learning.
imirror
to encourage learning it is important to establish curiosity and notion of possibility for more perspectives habit of questioning possibilities and cause and effect in a great way to encourage learning in my opinion. language is another important factor
imirror
under what schedule of reinforcement do animals learn from ?