What's you question?nukeman said:Homework Statement
Find the distance from the point (-2,3) to the centre of the circle x^2 + 2x + y^2 - 2y - 3 = 0
Homework Equations
The Attempt at a Solution
The circle, I calculated that the center point is (-1,1) is that correct?
Then, I just input it into the distance formula: √((-1+2)^2 + (1 - 3)^2 )
?
Yes, to both questions.nukeman said:Homework Statement
Find the distance from the point (-2,3) to the centre of the circle x^2 + 2x + y^2 - 2y - 3 = 0
Homework Equations
The Attempt at a Solution
The circle, I calculated that the center point is (-1,1) is that correct?
Then, I just input it into the distance formula: √(-1+2)^2 + (1 - 3)^2
?
The distance between two points can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values (x1 = -2, y1 = 3, x2 = -1, y2 = 1), we get:
d = √[(1)^2 + (-2)^2] = √(1 + 4) = √5
Therefore, the distance between (-2,3) and (-1,1) is √5 units.
To find the distance between two points on a coordinate plane, you can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Another way is to use the Pythagorean Theorem, where the distance is the hypotenuse of a right triangle formed by the two points and the x and y-axis.
You can also use a ruler or a measuring tool to physically measure the distance between the two points on the coordinate plane.
Yes, the distance between two points on a coordinate plane is always a positive value. This is because the distance formula involves squaring the differences between the coordinates, which eliminates any negative values.
Also, distance is a measure of length and cannot be negative.
If one of the coordinates of a point changes, the distance between the two points will also change.
For example, if we change the x-coordinate of (-2,3) to -4, the distance between (-2,3) and (-1,1) will increase since the distance formula takes into account the difference between x-coordinates.
However, if we change the y-coordinate of (-2,3) to 4, the distance between the two points will decrease since the difference between y-coordinates affects the distance formula.
Yes, the distance between two points can be zero if the two points are the same.
For example, the distance between (-2,3) and (-2,3) is zero since there is no difference between the two points.
Another scenario is if one of the points has coordinates (0,0), then the distance between that point and any other point will be equal to the distance between the other point and the origin, which is the distance from (0,0) to itself, which is also zero.