The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4) is:
(3, -10)
Given the center of the circle is (2, -3) and one endpoint B is (1, 4). Since AB is the diameter of the circle and the center is the midpoint of AB, we can find the coordinates of point A. Let the coordinates of A be (x, y).
The midpoint formula is:
Midpoint = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Substitute the given values:
Midpoint = ( (x+1)/2, (y+4)/2 )
We know the midpoint is the center of the circle, (2, -3). Therefore,
( (x+1)/2, (y+4)/2 ) = (2, -3)
Equating x-coordinates:
(x+1)/2 = 2
x+1 = 4
x = 3
Equating y-coordinates:
(y+4)/2 = -3
y+4 = -6
y = -10
Thus, the coordinates of point A are (3, -10).
The correct answer is (3, -10).
Important Questions from Co-ordinate Geometry
In which quadrant is the point (–4, –3) located?
A. I
B. II
C. III
D. IV
The area of a quadrilateral whose vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order, is:
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
In ΔABC if ∠A = 50° and ∠B = 70°, find the measure of exterior angle A.
