Answer
Verified
393.3k+ views
Hint: Here, we have to find the coordinate of \[A\], for that we use the formula for midpoint.
First we have to find Coordinate of the \[x\] axis and \[y\] axis.
Finally we get the required answer.
Complete step-by-step answer:
It is given that the circle with centre \[{\text{C}}(2, - 3)\] and \[AB\] is the diameter of circle with \[B(1,4)\]
We have to find the coordinates of a point \[A\].
Let we consider \[(x,y)\] to be the coordinate of \[A\].
Since \[AB\] is the diameter of the circle,
Here, centre \[C\] is the midpoint of \[AB\]
\[x - \]Coordinate of centre = \[\dfrac{{{x_1} + {x_2}}}{2}\]
\[y - \]Coordinate of centre= \[\dfrac{{{y_1} + {y_2}}}{2}\]
\[{x_1} = x\], \[{y_1} = y\], \[{x_2} = 1\],\[{y_2} = 4\]
\[x - \] Coordinate of centre = \[\dfrac{{x + 1}}{2}\]
\[y - \] Coordinate of centre = \[\dfrac{{y + 4}}{2}\]
But given that centre of circle is \[(2, - 3)\] named as \[(x,y)\]
Therefore, we can write it as
\[x - {\text{Coordinate}}\]
\[\dfrac{{x + 1}}{2} = 2\]
after cross multiplication, we get
\[x + 1 = 4\]
Taking the term $1$ as RHS,
\[x = 4 - 1\]
On subtracting we get,
\[x = 3\]
Also we can write it as,
\[y - \]Coordinate
\[\dfrac{{y + 4}}{2} = - 3\]
after cross multiplication, we get
\[y + 4 = - 6\]
Taking the terms $4$ as RHS,
\[y = - 6 - 4\]
On subtracting we get,
\[y = - 10\]
Thus, the coordinate of \[A\] is \[(3, - 10)\]
Hence the answer is \[(3, - 10)\]
Note: The above sum is the centre and a point is given, ask to find the other coordinate, mostly questions will be asked about what is the centre of the circle when the two points given, for that we use the above formula to derive the sum.
The coordinates we chosen for \[A\] is \[(x,y)\],
Suppose point \[A\] is given and we have to find centre \[C\], it is very easy use
\[x - \] Coordinate of centre = \[\dfrac{{{x_1} + {x_2}}}{2}\] to find \[x - \] coordinate of centre.
Similarly, \[y - \] coordinate of centre = \[\dfrac{{{y_1} + {y_2}}}{2}\] to find \[y - \] coordinate of centre.
Hence the centre is obtained.
First we have to find Coordinate of the \[x\] axis and \[y\] axis.
Finally we get the required answer.
Complete step-by-step answer:
It is given that the circle with centre \[{\text{C}}(2, - 3)\] and \[AB\] is the diameter of circle with \[B(1,4)\]
We have to find the coordinates of a point \[A\].
Let we consider \[(x,y)\] to be the coordinate of \[A\].
Since \[AB\] is the diameter of the circle,
Here, centre \[C\] is the midpoint of \[AB\]
\[x - \]Coordinate of centre = \[\dfrac{{{x_1} + {x_2}}}{2}\]
\[y - \]Coordinate of centre= \[\dfrac{{{y_1} + {y_2}}}{2}\]
\[{x_1} = x\], \[{y_1} = y\], \[{x_2} = 1\],\[{y_2} = 4\]
\[x - \] Coordinate of centre = \[\dfrac{{x + 1}}{2}\]
\[y - \] Coordinate of centre = \[\dfrac{{y + 4}}{2}\]
But given that centre of circle is \[(2, - 3)\] named as \[(x,y)\]
Therefore, we can write it as
\[x - {\text{Coordinate}}\]
\[\dfrac{{x + 1}}{2} = 2\]
after cross multiplication, we get
\[x + 1 = 4\]
Taking the term $1$ as RHS,
\[x = 4 - 1\]
On subtracting we get,
\[x = 3\]
Also we can write it as,
\[y - \]Coordinate
\[\dfrac{{y + 4}}{2} = - 3\]
after cross multiplication, we get
\[y + 4 = - 6\]
Taking the terms $4$ as RHS,
\[y = - 6 - 4\]
On subtracting we get,
\[y = - 10\]
Thus, the coordinate of \[A\] is \[(3, - 10)\]
Hence the answer is \[(3, - 10)\]
Note: The above sum is the centre and a point is given, ask to find the other coordinate, mostly questions will be asked about what is the centre of the circle when the two points given, for that we use the above formula to derive the sum.
The coordinates we chosen for \[A\] is \[(x,y)\],
Suppose point \[A\] is given and we have to find centre \[C\], it is very easy use
\[x - \] Coordinate of centre = \[\dfrac{{{x_1} + {x_2}}}{2}\] to find \[x - \] coordinate of centre.
Similarly, \[y - \] coordinate of centre = \[\dfrac{{{y_1} + {y_2}}}{2}\] to find \[y - \] coordinate of centre.
Hence the centre is obtained.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE