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प्रश्न
If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:
पर्याय
A. (−6, 7)
B. (6, −7)
C. (6, 7)
D. (−6, −7)
उत्तर
Let AB be the diameter and O be the centre of the circle.
We are given co-ordinates of one end point of circle and co-ordinates of its centre.
So, co-ordinates of A are (2, 3) and centre O are (−2, 5).
Let co-ordinates of point B be (x, y).
We know that centre of a circle is the midpoint of the diameter.
∴ By midpoint formula,
`-2=(2+x)/2` and `5=(3+y)/2`
`rArr=-4=2+`and`10=3+y`
`rArrx=-6`and`y=7`
So, other end of the diameter is (−6, 7).
Hence, the correct answer is A.
संबंधित प्रश्न
In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.
AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7), find
- the length of radius AC.
- the coordinates of B.
The three vertices of a parallelogram ABCD are A(3, −4), B(−1, −3) and C(−6, 2). Find the coordinates of vertex D and find the area of ABCD.
In what ratio is the line joining (2, -4) and (-3, 6) divided by the line y = O ?
Find the ratio in which the line x = O divides the join of ( -4, 7) and (3, 0).
Also, find the coordinates of the point of intersection.
Find the points of trisection of the segment joining A ( -3, 7) and B (3, -2).
A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively ______.
If P(9a – 2, – b) divides line segment joining A(3a + 1, –3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1
Read the following passage:
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. |
Based on the above information, answer the following questions :
- Taking O as origin, coordinates of P are (–200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S?
- (a) What is the area of square PQRS?
OR
(b) What is the length of diagonal PR in square PQRS? - If S divides CA in the ratio K : 1, what is the value of K, where point A is (200, 800)?
