The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3) ______.

The ratio in which the x-axis divides the line segment joining the points A(a₁, b₁) and B(a₂, b₂ ) is ______.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

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 ______.

The centroid of the triangle with vertices (−1, −6), (−2, 12) and (9, 3) is

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 mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle.

The points A(−3, 6), B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

Prove that the diagonals of the parallellogram bisect each other. [Hint: Take scale on both axes as 1 cm = a units]

In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9) .

The line segment joining A(6, 3) and B(−1, −4) is doubled in length by adding half of AB to each end. Find the coordinates of the new end points.

A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

If the centroid of a triangle is at (4, −2) and two of its vertices are (3, −2) and (5, 2) then find the third vertex of the triangle.

If  \(\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right) \)and\((\frac{13}{2},\frac{-13}{2})\) are mid-points of the sides of a triangle, then find the centroid of the triangle.

The point (3, −4) is the centre of a circle. If AB is a diameter of the circle and B is (5, −6), find the coordinates of A.

If (x, 3), (6, y), (8, 2) and (9, 4) are the vertices of a parallelogram taken in order, then find the value of x and y.

Find the points which divide the line segment joining A(−11, 4) and B(9, 8) into four equal parts.

Find the centroid of the triangle whose veritices are A(6, −1), B(8, 3) and C(10, −5).

If the centroid of a triangle is at (−2, 1) and two of its vertices are (1, −6) and (−5, 2), then find the third vertex of the triangle.

The mid-points of the sides of a triangle are (5, 1), (3, −5) and (−5, −1). Find the coordinates of the vertices of the triangle.

What are the coordinates of B if point P(−2, 3) divides the line segment joining A(−3, 5) and B internally in the ratio 1 : 6?