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______.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

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

A(−3,2), B(3,2) and C(−3,−2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.

A car travels at an uniform speed. At 2 pm it is at a distance of 180 km and at 6pm it is at 360 km. Using section formula, find at what distance it will reach 12 midnight.

ABC is a triangle whose vertices are A(3, 4), B(−2, −1) and C(5, 3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

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.

the mid-point formula to show that the mid-point of the hypotenuse of a right angled triangle is equidistant from the vertices (with suitable points).

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.

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.