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Co-Ordinate Geometry..

Hello TSR,

I have to complete an assignment by monday on all of the work we have learned so far in maths...

But i am slightly confused with some questions and i would much appreciate some help!!

** The points A,B,C have coordinates (-2,3), (10,-1), (3,8) respectively. The line through C prpendicular to AB, intersect AB at point D.

Show that AB has equation x + 3y - 7 = 0 --- WHICH I HAVE DONE

But then it asks find the equation of CD and i have no clue what to do here...

Also show that d has coordinates (1,2) and basically i don't know how to work it out, as my literacy skills and very good and i don't understand what the question is telling me about D.

and then... Th midpoint of AB is denoted by E. Find the length of ED.
Any help please...

Help would be much appreciated... Thans in advance!! :s-smilie:

Scroll to see replies

Reply 1

apo1324

Sorry to bother people... :frown:

Reply 2

amongsttheweeds

Use the equation (y2-y1) = m(x2-x1) I think. Do you know how to use this?

Edit: can you find point D?

Reply 3

apo1324

ino how to use it but y do i use it to work out CD?? bec i can't find the gradient with 1 point

Reply 4

apo1324

Any ideas please.. :frown:

Reply 5

apo1324

To find the equation of CD

do i form y=mx+c then sub in the points etc... then use y-y(1)=m(x-x(1)) ??

Reply 6

amongsttheweeds

apo1324

ino how to use it but y do i use it to work out CD?? bec i can't find the gradient with 1 point

It says that the line intersects point D passes through C. Also, the line is perpendicular to line AB If it's perpendicular, the gradients will multiply together to get -1. Therefore:
m1 x m2 = -1

Sub m1 in (you can work this out; the gradient of AB), solve the equation for m2, and there's your gradient for CD. :smile:

Reply 7

apo1324

Sooo the gradient for AB = -0.3??

Reply 8

apo1324

m = (y2-y1)/(x2-x1)
= (-1-3)/(10+2) = -4/+12 = -0.33333

Reply 9

apo1324

therefore -0.3 multiply by 3 = -1

so m2 = 3?? :frown:

I suck at this

Reply 10

amongsttheweeds

apo1324

Sooo the gradient for AB = -0.3??

You said:
AB has equation x + 3y - 7 = 0

So from looking at it I think it's -1/3x. You rearrange into the y = mx + c form in order to find m1 (the gradient) and then put it into m1 x m2 = -1

Reply 11

amongsttheweeds

apo1324

therefore -0.3 multiply by 3 = -1

so m2 = 3?? :frown:

I suck at this

That's right. :biggrin:

Reply 12

apo1324

so the equation for cd would be:-

y-y1=m(x-x1)
y-8=3(x-3)
y-8=3x-9
y=3x-1?? equation for cd

Reply 13

amongsttheweeds

apo1324

so the equation for cd would be:-

y-y1=m(x-x1)
y-8=3(x-3)
y-8=3x-9
y=3x-1?? equation for cd

Looks right!

Now, to show that point D has the co-ordinates (1,2) you simply substitute those co-ordinates into those equations (as AB and CD intersect at point D).

Reply 14

apo1324

what will the answers show tho??

Reply 15

apo1324

because they will come up with different answers, so how do i know they are right

Reply 16

amongsttheweeds

apo1324

because they will come up with different answers, so how do i know they are right

Do it and see what you get. You should be able to see. :wink:

Reply 17

apo1324

do i substitute both of them into both equations??

Reply 18

amongsttheweeds

apo1324

do i substitute both of them into both equations??

Yeah, x=1 and y=2. :smile:

Reply 19

apo1324

ok...
y=3x-1 (x=1)
y=3(1)-1 = 3 - 1 = 2 (1,2)

y=3x-1 (y=2)
2=3x-1
2+1=3x
3/3=x
x=1 (1,2)

x+3y-7=0 (x=1)
1+3y-7=0
3y=-1+7
3y=+6
y=+6/3
y=2 (1,2)

x+3y-7=0 (y=2)
x+3(2)-7=0
x+6-7=0
x-1=0
x=1 (1,2)

Are they correct??