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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:
विकल्प
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
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order.
[Hint: Area of a rhombus = `1/2` (product of its diagonals)]
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.
If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.
Show that the line segment joining the points (–5, 8) and (10, −4) is trisected by the co-ordinate axes.
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 perpendicular bisector of the line segment joining the points A(1, 5) and B(4, 6) cuts the y-axis at ______.
Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.
Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.
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)?
