Advertisements
Advertisements
Question
Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.
Solution
Centre = P(–2, 0)
Diameter has A(2, –3) on one end and B(x, y) on the other.
The centre point P divides AB in two equal parts.
So, using the midpoint formula,
\[- 2 = \frac{2 + x}{2}\]
\[ \Rightarrow - 4 = 2 + x\]
\[ \Rightarrow x = - 6\]
\[\text { And }\]
\[0 = \frac{- 3 + y}{2}\]
\[ \Rightarrow 0 = - 3 + y\]
\[ \Rightarrow y = 3\]
\[\left( x, y \right) = \left( - 6, 3 \right)\]
APPEARS IN
RELATED QUESTIONS
ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find
1) Coordinates of A
2) An equation of diagonal BD
A(5, 3), B(–1, 1) and C(7, –3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that : `LM = 1/2 BC`.
In the given figure, P(4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.
One end of the diameter of a circle is (–2, 5). Find the co-ordinates of the other end of it, if the centre of the circle is (2, –1).
A(2, 5), B(1, 0), C(−4, 3) and D(–3, 8) are the vertices of quadrilateral ABCD. Find the co-ordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.
Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).
Find the midpoint of the line segment joining the following pair of point :
( -3, 5) and (9, -9)
If the midpoints of the sides ofa triangle are (-2, 3), (4, -3), (4, 5), find its vertices.
A( 4, 2), B(-2, -6) and C(l, 1) are the vertices of triangle ABC. Find its centroid and the length of the median through C.
The coordinates of the end points of the diameter of a circle are (3, 1) and (7, 11). Find the coordinates of the centre of the circle.
If P(–b, 9a – 2) divides the line segment joining the points A(–3, 3a + 1) and B(5, 8a) in the ratio 3: 1, find the values of a and b.
As shown in the figure. two concentric circles are given and line AB is the tangent to the smaller circle at T. Shown that T is the midpoint of Seg AB
Point M is the mid-point of segment AB. If AB = 8.6 cm, then find AM.
Find the mid-point of the line segment joining the points
(−2, 3) and (−6, −5)
The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7) then find the other end
The ratio in which the x-axis divides the line segment joining the points A (a1, b1) and B (a2, b2) is
If (1, −2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is
Find the coordinates of point P where P is the midpoint of a line segment AB with A(–4, 2) and B(6, 2).
Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
