determine the sets of points whos distances from (-2,2) and (3,-3) are in the ratio of 2:3
Im clueless.....
Im clueless.....
math qr question
- Thread starter spoog74
- Start date
- Joined
- May 1, 2011
- Messages
- 217
- Reaction score
- 2
I would use the given answers and plug and chug with the distance formula; finding the distance between each of those points and seeing if its in a 2:3 ratio.
Pick the middle-most point and then adjust accordingly to get the correct ratio.
I am sure there is another way to do this, but thats the first thing that I thought of and if you get to QR you just need to go through the questions as quick as possible. There is probably a quicker/easier way to do it than that, but if you factor in the time it takes to remember that formula and apply it this way could be faster and just as effective.
Hope that helps
- Joined
- Jan 12, 2011
- Messages
- 545
- Reaction score
- 155
Suppose (x,y) is the point who distance from (-2,2) and (3,-3) is the ratio 2:3
Use the Distance formulae for both of them i.e (x,y) & (-2,2) and (x,y) & (3,-3)
For (x,y) and (-2,2) using distance formula
√{[x - (-2)]^2 + (y - 2)^2}
For (x,y) and (3,-3)
√{(x - 3)^2 + [y - (-3)]^2}
Now since the sides are in ratio 2/3
[√{[x - (-2)]^2 + (y - 2)^2}}]/[√{(x - 3)^2 + [y - (-3)]^2}] = 2/3
Doing your cross multiplication and squaring both sides ( squaring comes 1st before x-multiply) you will end up with in equation below
(x^2 + 12x + 36) + (y^2 - 12y + 36) = 36 + 36
The reason im writing this step is because you will be tempted to Cancel out the 36's. Dont do that
Further Simplification gives you
(x + 6)^2 + (y - 6)^2 = (√72)^2
Points are x=-6 and y= 6. i.e (-6, 6)
Note this is an equation of a circle with a radius of √72 [Just for extra info 🙂]
Hope this is what your looking for...
Use the Distance formulae for both of them i.e (x,y) & (-2,2) and (x,y) & (3,-3)
For (x,y) and (-2,2) using distance formula
√{[x - (-2)]^2 + (y - 2)^2}
For (x,y) and (3,-3)
√{(x - 3)^2 + [y - (-3)]^2}
Now since the sides are in ratio 2/3
[√{[x - (-2)]^2 + (y - 2)^2}}]/[√{(x - 3)^2 + [y - (-3)]^2}] = 2/3
Doing your cross multiplication and squaring both sides ( squaring comes 1st before x-multiply) you will end up with in equation below
(x^2 + 12x + 36) + (y^2 - 12y + 36) = 36 + 36
The reason im writing this step is because you will be tempted to Cancel out the 36's. Dont do that
Further Simplification gives you
(x + 6)^2 + (y - 6)^2 = (√72)^2
Points are x=-6 and y= 6. i.e (-6, 6)
Note this is an equation of a circle with a radius of √72 [Just for extra info 🙂]
Hope this is what your looking for...
- Joined
- Jan 12, 2011
- Messages
- 545
- Reaction score
- 155
True...its long...which is why i would mark this and do everything else, otherwise ull waste time getting this answer rite and running out of time with other problems...
Do questions like this at the end, if ur running out of time, just make an educated guess
Do questions like this at the end, if ur running out of time, just make an educated guess
- Joined
- May 11, 2011
- Messages
- 4
- Reaction score
- 0
what were the choices?
Cause i feel like every point on y = x should be 2:3 ratio with (2,-2) and (3,-3)
Cause i feel like every point on y = x should be 2:3 ratio with (2,-2) and (3,-3)
Nope. The point (100, 100), for example, lies on y = x and it's basically the same distance from both (-2, 2) and (3, -3)...I say "basically" because you don't have to actually run the numbers to know that a 2:3 ratio is not happening.
