Question

I really need help with this exercise please help me asap.

Answer 1

ok, try A first

Answer 2

mhm

Answer 3

translate means "move"

Answer 4

so what do you get when you move A 4 units horizontally and -2 units vertically?

Answer 5

2:1 ?

Answer 6

yes, exactly!

Answer 7

next B. you want to make it a mirror image about the X axis, which means imagine folding the paper in half with the x axis as the crease

Answer 8

thank man so b would be 1;3 ?

Answer 9

yes exactly! to reflect something about the x axis, the x coordinate stays the same, and the y coordinate is negative of whatever it was originally.

Answer 10

let's do D next and leave C for last. it's almost the same as B, except around the Y axis instead of X.

Answer 11

sweet and symetrical is ?

Answer 12

huh ?

Answer 13

ahhh okay i kinda understand

Answer 14

it's just like B, pretend you're folding the paper, but this time the crease is the Y axis

Answer 15

-2:-1 ?

Answer 16

close - i think you're looking at point C instead of D.

Answer 17

point D is the one we want to reflect about the Y axis

Answer 18

(i left C for last because it's different)

Answer 19

oh okay so d would be 4;2 ?

Answer 20

almost. it would be 4; -2

Answer 21

it's -4;-2 now, so reflecting it around the Y axis would give you 4;-2

Answer 22

yeh sorry XD i saw that now

Answer 23

and c how would i do c ?

Answer 24

ok now let's go back and do C. this one is a little harder to visualize; where does C go if you fold the paper using that line x=y as the crease?

Answer 25

the way you reflect things about that line is by reversing the X and Y coordinates, i.e. swapping them.

Answer 26

-2;1 ?

Answer 27

not quite -- you're negating each one, but for this special case what you do is swap them

Answer 28

make the first one into the second, and vice versa

Answer 29

so.. 1;-2 ?

Answer 30

nope ... all you do is reverse the order. it's at 2;-1, so the point reflected would be -1;2

Answer 31

all i did was reverse the two coordinates. that's how you reflect something around the special line x=y

Answer 32

aahhhh omg yeh i see now thanks

Answer 33

thanks would you mind explaining some other questions to me ?

Answer 34

ok

Answer 35

A(-1;3),B(3;-2),C(6;1),D(2;6) are the vertices of quadrilatera; ABCD
calculate the midpoints of AC and BD
The lengths of AD and BC
The gradients of AB and DC

Answer 36

i have no idea how todo this one would you mind explaining it to me ?

Answer 37

ok well, to find midpoints, you just average the X and Y coordinates (separately)

Answer 38

erm... which is how ?
Like how do you avarage them ?

Answer 39

so the midpoint of AC's x coordinate is the average of A's x coordinate and C's x coordinate, i.e. add them together and divide by 2. then do the same for Y.

Answer 40

so...
-1+6 =5
5/2 = 2.5

3+1 = 4
4/2 = 2

Answer 41

yep you got it

Answer 42

so then the awnser would be (2.5;2) ?

Answer 43

yep

Answer 44

so AC = (2.5;2)

3+2= 5
-2+6 = 4

BD=(5;4)

Answer 45

you forgot to divide by 2 on that one

Answer 46

pellet yeh um
So AC=(2.5;2)
BD = (2.5;2)

Answer 47

yep, they came out the same, since you found the midpoint of the two diagonals and they intersect in the center of the figure

Answer 48

cool its just to see that the awnsers right how about figuring out the lengths ??

Answer 49

ad and bc ?

Answer 50

then you use the distance equation, are you familiar with it?

Answer 51

Nope

Answer 52

Im a noob at math >.>

Answer 53

if you have a textbook they must have this equation in there somewhere, it's kind of unreasonable for them to expect you to work it out on your own. the distance equation is:

Answer 54

thats the reason i cant do this is because my txt book is at school :/

Answer 55

\[\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\]

Answer 56

exams are coming up so im doing revision

Answer 57

so to find the distance you plug the x and y values of the two points into that formula i just gave you

Answer 58

okay so thats 29 then ?

Answer 59

which points are you computing

Answer 60

yehp just did that \[\sqrt{?}\](-1-3)^2(3--2)^2

Answer 61

which equals 29

Answer 62

-1-3 = -4, squared is 16
3--2 is 5, squared is 25

Answer 63

D: oh okay so its 41 then ?

Answer 64

wait hold on, let me find your original coordinates ... you're doing AD right?

Answer 65

ad and bd

Answer 66

bc **

Answer 67

so that's (-1; 3) to (2; 6)
-1 -2 == -3, squared is 9
3 - 6 = -3, squared = 9
added together is 18
so distance is sqrt(18)

Answer 68

okay but dont we still have todo bc ?

Answer 69

yes, so do that the same way

Answer 70

kk one sec

Answer 71

(3;-2) to (6;1)
3 -2 = 1, squared is 1
3 - 6 = -3, squared = -9
added together is -8 so distance is sqrt(-8)

Answer 72

well remember that whnever you square something it coems out positive, -3 squared is +9

Answer 73

also, subtracting a negative number is like adding. 3 - (-2) is like 3+2

Answer 74

and remember you're comparing x's, then comparing y's
so 3 - 6 = -3, squared is 9
-2 minus 1 is also -3, squared is 9

Answer 75

no wait its wrong because its supose to be 3-6 = -3 sqrd = 9 and -2 - 1 = -3 sqrd = 9

Answer 76

9+9 = 18 :D

Answer 77

yep, so it's sqrt(18), i.e. \[\sqrt{18}\]

Answer 78

lol only just realised thats exactly what you said but i saw the rpoblem in my own equation Hahaha sorry

Answer 79

that's way better than me telling you anyway :-)

Answer 80

just curious, what grade are you in?

Answer 81

and finally the last one ? what do they meen the gradoents ?just wat they said on the top or ?

Answer 82

well gradient is another name for slope. do you now how to compute the slope of a line?

Answer 83

oh lol im in grade 9 From South africa thats not me in the profile pic its just a cartoon char why do you ask ?

Answer 84

no sorry i dont :/

Answer 85

well slope is "rise over run", meaning how far it goes up for each unit of distance horizontally. so if you have two points you can compute the slope as
\[{y_2-y_1 \over x_2-x_1}\]

Answer 86

aaahk ill try it now

Answer 87

\[-2-3/ 3--1\]

Answer 88

=-5
-
2
?

Answer 89

which slope are you computig?

Answer 90

AB

Answer 91

let's see, -2 -3 for Y is -5
3 - -1 = 4 for x
so I get -5/4

Answer 92

ahh right yeh >.<

Answer 93

then DC would be
6-2 = 4
1-5 = -4
4/-4 ?

Answer 94

i think C is (6; 1) right? and
D (2; 6)?

Answer 95

omg im such a retard.

Answer 96

yeh its a 6 -.-