Question

Coordinate Geometry Help *question attached below* MEDAL WILL BE AWARDED

Answer 1

In the diagram below, not drawn to scale, the line 2x+3y=6 meets the y-axis at A and the x-axis at B. C is the point produced such that B is the mid-point of AC.
(a) Find the coodrinates of A, B and C.
(b) Find an equation of the line CD through C perpendicular to AB.

Answer 2

Do you know where to start with this problem? Or have you found some information but stuck at some part?

Answer 3

I have found A, which is (0,2), but I am stuck at finding B.

Answer 4

A = (0,2) is correct.
B is said to be the point where the line crosses the x-axis. Similar to the y-axis whose line is x=0, the x-axis is the line y=0.

Answer 5

So you're looking for the point (x, 0) on the line 2x + 3y = 6. Does that seem any more clear?

Answer 6

I am still lost :S

Answer 7

Oh wait! I got it!

Answer 8

To find the x-intercept..I just substitute 0 for y, which gives 3(0)+2x=6. Therefore, x is equal to 3 so the coordinates of B are (3,0)?

Answer 9

Yes! :)

Answer 10

How do I approach to find the coordinates of C? Do I have to use the fact that B is the midpoint?

Answer 11

Yes, that is the key piece of information. If you recall the midpoint formula, you now know points A and B. You would just have to solve for the information of C. :)

Answer 12

Hmm, I know the midpoint formula, but I don't know how to use that to find C. I was thinking, what if I count the distance between A and B, and since I know B is the midpoint, count the same number of units to C?

Answer 13

Or let me try to think of how to use the mid-point for a second

Answer 14

Yes, the distance formula idea may work but it may be a lot more work than the midpoint formula would be.

Answer 15

Alright..I have no idea what to do

Answer 16

I think I got it.

Answer 17

Since I know the coordinates for B are (3,0), and I know the midpoint formula..can I say (x+0/2)=3 (x coordinate for B. Therefore, x=6 and (y+2/2)=0 therefore, y =-2? So the coordinates for C are (6,-2)?

Answer 18

That looks good to me.
You can confirm just by reapplying the midpoint formula of A and C to get B again. :)

Answer 19

Yes! :)

Answer 20

So that completes part (a), all that is left is part (b) and finding the perpendicular line to AB containing C.

Answer 21

I know how to find that. I found the gradient of AB, which is -2/3. To get the gradient of CD, I make the gradient for AB the negative reciprocal. using the coordinates C(6,-2), I substitute that along with the gradient of CD in the equation of the line..and I ended up with 2y=3x-22

Answer 22

The gradient of CD I found was 3/2

Answer 23

Excellent, that is all correct to me. Good work! :D

Answer 24

Thank you! I couldn't have made it that far without you explaining the bit :)

Answer 25

Glad to be able to help a bit! :P
Apologies for slow responses, got band-aids on my fingers making it awkward to type! lol

Answer 26

It's alright :)