Advertisements
Advertisements
प्रश्न
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–2, –5), Q(4, 3), a : b = 3 : 4
उत्तर
Let the coordinates of point A be (x, y).
P(–2, –5), Q(4, 3), a : b = 3 : 4
Using section formula
\[x = \frac{3 \times 4 + 4 \times \left( - 2 \right)}{3 + 4} = \frac{12 - 8}{7} = \frac{4}{7}\]
\[y = \frac{3 \times 3 + 4 \times \left( - 5 \right)}{3 + 4} = \frac{9 - 20}{7} = \frac{- 11}{7}\]
\[\left( x, y \right) = \left( \frac{4}{7}, \frac{- 11}{7} \right)\]
APPEARS IN
संबंधित प्रश्न
A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.
The mid-point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a + 1). Find the values of a and b.
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(2, 6), Q(–4, 1), a : b = 1 : 2
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.
Find the coordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).
Write the co-ordinates of the point of intersection of graphs of
equations x = 2 and y = -3.
Find the midpoint of the line segment joining the following pair of point :
( a+3, 5b), (3a-1, 3b +4).
Find the midpoint of the line segment joining the following pair of point :
(a+b, b-a) and (a-b, a+b)
If the midpoints of the sides ofa triangle are (-2, 3), (4, -3), (4, 5), find its vertices.
AB is a diameter of a circle with centre 0. If the ooordinates of A and 0 are ( 1, 4) and (3, 6 ). Find the ooordinates of B and the length of the diameter.
A(3, 1), B(y, 4) and C(1, x) are vertices of a triangle ABC. P, Q and R are mid - points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid ΔABC.
If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?
O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.
If the coordinates of one end of a diameter of a circle is (3, 4) and the coordinates of its centre is (−3, 2), then the coordinate of the other end of the diameter is
Point P is midpoint of segment AB where A(– 4, 2) and B(6, 2), then the coordinates of P are ______
Find coordinates of midpoint of the segment joining points (0, 2) and (12, 14)
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
If the vertices of a triangle are (1, 3), (2, - 4) and (-3, 1). Then the co-ordinate of its centroid is:
Find the co-ordinates of centroid of a triangle if points D(–7, 6), E(8, 5) and F(2, –2) are the mid-points of the sides of that triangle.
Find the coordinates of the mid-point of the line segment with points A(– 2, 4) and B(–6, –6) on both ends.
