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# Surds on a graph watch

1. I'm really confused by this question and have attempted it so many times but have gotten it wrong every time.

Here it is:
Point A is (1,1)
Point B is 2√10 units from A and lies on the intersection of two grid lines.
Write the coordinates of both possible positions for B.

I don't know how to even start. Can someone help please?
2. (Original post by Siliac)
I'm really confused by this question and have attempted it so many times but have gotten it wrong every time.

Here it is:
Point A is (1,1)
Point B is 2√10 units from A and lies on the intersection of two grid lines.
Write the coordinates of both possible positions for B.

I don't know how to even start. Can someone help please?
let's call the co-ordinates of B (c, d). So using the info about units, you can set up one equation... (think about working out the distance between two points)

Now the grid line info bit, I think wants you to use the fact that the co-ordinates are both integers. So if I had two integers c and d, there is some number k such that c = kd. For example, if we found c = 10, d = 2 then k = 5. Similarity, if c = 2 and k = 3 then d = 2/3.

So how can you use that c = kd?
3. (Original post by Kevin De Bruyne)
let's call the co-ordinates of B (c, d). So using the info about units, you can set up one equation... (think about working out the distance between two points)

Now the grid line info bit, I think wants you to use the fact that the co-ordinates are both integers. So if I had two integers c and d, there is some number k such that c = kd. For example, if we found c = 10, d = 2 then k = 5. Similarity, if c = 2 and k = 3 then d = 2/3.

So how can you use that c = kd?
I don't know how exactly I can use the c = kd. I've tried using Pythagoras because it's on a graph so it should be able to be used to get more information that I could use with c = kd but I don't think that it's going to be very useful at all.

(c-1)^2 + (d-1)^2 = (2√10)^2
(c-1)^2 = (2√10)^2 - (d-1)^2
c^2 - 2c + 1 = 40 - (d^2 - 2d + 1)
c^2 - 2c + 1 = 40 - d^2 + 2d - 1
c^2 - 2c + 1 = 39 - d^2 + 2d
c^2 - 2c = 38 - d^2 + 2d
4. (Original post by Siliac)
I don't know how exactly I can use the c = kd. I've tried using Pythagoras because it's on a graph so it should be able to be used to get more information that I could use with c = kd but I don't think that it's going to be very useful at all.

(c-1)^2 + (d-1)^2 = (2√10)^2
(c-1)^2 = (2√10)^2 - (d-1)^2
c^2 - 2c + 1 = 40 - (d^2 - 2d + 1)
c^2 - 2c + 1 = 40 - d^2 + 2d - 1
c^2 - 2c + 1 = 39 - d^2 + 2d
c^2 - 2c = 38 - d^2 + 2d
Hmm... that didn't lead where I thought it would. Sorry!
5. (Original post by Siliac)
I'm really confused by this question and have attempted it so many times but have gotten it wrong every time.

Here it is:
Point A is (1,1)
Point B is 2√10 units from A and lies on the intersection of two grid lines.
Write the coordinates of both possible positions for B.

I don't know how to even start. Can someone help please?
You have a coordinate of B on the x axis and another on the y axis so you have coordinates (0,p) and (p,0). (p is a random letter btw) You know that A is either 1 across from B or 1 above B and you also know that the total distance is 2sqrt10. Can you use these two numbers to find the other distance?
6. (Original post by Siliac)
I'm really confused by this question and have attempted it so many times but have gotten it wrong every time.

Here it is:
Point A is (1,1)
Point B is 2√10 units from A and lies on the intersection of two grid lines.
Write the coordinates of both possible positions for B.

I don't know how to even start. Can someone help please?
You can create a circle of points which are a distance of from the point by saying that the equation of it is (around the point ))

Now, you want to just pick two pairs of numbers such that are whole numbers that satisfy .

Once you find them, the coordinates of B are just for each pair.

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Updated: November 12, 2017
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