Question

ABCD is a square where A is the point (0,2) and C is the point (8,4). AC and BD are diagonals of the square and they intersect at E. Find the coordinates of B and D.

Answer 1

I have found out the coordinate of E which is(4,3) and the equation of Bd and length of AE

Answer 2

slope is 1/4?

Answer 3

so perp slope is -4

Answer 4

the ans for the coordinate of B is(5,-1) & D is (3,7)

Answer 5

but i do not know how to derive at it

Answer 6

the slope form a to c aint 1 so its not a square that situated nicely like that is it?

Answer 7

slope from a to c is: 2/8 = 1/4

Answer 8

ABCD is a square in the question

Answer 9

e is a+c/2 for midpoint

8,4
0,2
----
8,6 /2 = 4,3 e is good

Answer 10

y=-4x+4(4)+3

y=-4x+19 is the equation of the line perp to ac and thru 4,3

Answer 11

hmmm, so. ; this laptop doesnt make this easier lol

Answer 12

we need a vector that is the length of ae

Answer 13

its \[\sqrt{17}\] length of ae

Answer 14

8,4
-4,3
----
<4,1>; mag = sqrt(17) that ougt to be fun to play with

Answer 15

i cant find a way to find the coordinate through the length of ae LOL

Answer 16

so the vector representation of say eb is our -4/1 slope

Answer 17

<1,-4> is out vector ... duh lol

Answer 18

form e move 1,-4 and -1,4 to get to the other corners

Answer 19

i was tinking of finding the coordinate through the x-axis difference and y-axis difference but it doesnt seem to work

Answer 20

4,3
1,-4
-----
5,-1


4,3
-1,4
-----
3,7

Answer 21

i get it thx:) alot

Answer 22

took a bit my my brain clicked lol

Answer 23

So what were the correct points? For some reason, I'm getting (3,7) and (5,-1), but the question is which one is B and which one is D

Answer 24

Hi im very sorry could you explain what is a vector?

Answer 25

a vector can be represented as a directed line segment; something like an arrow with distance and direction defines a vector

Answer 26

how did u arrive at a vector of (-1,4)

Answer 27

the slope of a line IS its vector i took the slope of the line from A to C

Answer 28

not drawn correctly in this pic, but same concept nonetheless

Answer 29

gradient AC= 1/4 thus the vector is (-1,4 ) and gradient AB= 4 vector is (-4,1)?

Answer 30

the slope of the line from A to C is:

C (8,4)
-A (0,2)
--------
8, 2 ; slope = 2/8; 1/4

the vector from A to C is then <4 , 1>

Answer 31

a vector is notated the same as a point, except for the < > parts that indicate it as a vector.

it is 4 wide and 1 tall; the components of its gradient (slope)

Answer 32

How did u get
C (8,4)
-A (0,2)
--------
8, 2

Answer 33

its called subtraction

Answer 34

8-0 , 4-2

these are the parts of the slope formula

Answer 35

its just easier for me to do them in this way then to try and sort out what goes where when its already done

Answer 36

but to be clear about the vector from A to C, I was a little off in my explaining.

The vector from A to C is actually <8,2>; half of this is going to be to the midpoint of E, since a midpoint is in the middle

<8,2>
------ = <4,1>, is our vector from A to E
2

Answer 37

i see thank you i will try to understand & do the question first, if I still do not understand could I still look for you? thx::)