Point Questions

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

If (3, -4) and (-6, 5) are the extremities of a diagonal of a parallelogram and (2, 1) is its third vertex, then its fourth vertex is -

The ratio in which the line joining the points (3, -4) and (-5, 6) is divided by x-axis -

The circumcentre of the triangle with vertices (0, 0), (3, 0) and (0, 4) is -

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12) then orthocentre of this triangle is -

Area of a triangle whose vertices are (a cos θ, b sin θ), (-a sin θ, b cos θ) and (-a cos θ, - b sin θ) is -

The point A divides the join of the points (-5, 1) and (3, 5) in the ratio k : 1 and coordinates of points B and C are (1, 5) and (7, -2) respectively. If the area of ᐃABC be 2 units, then k equ...

If A (cos α, sin α), B (sinα, - cosα), C (1, 2) are the vertices of a ᐃABC, then as α varies, the locus of its centroid is -

The points with the co-ordinates (2a, 3a), (3b, 2b) & (c, c) are collinear -

A stick of length 10 units rests against the floor and a wall of a room. If the stick begins to slide on the floor then the locus of its middle point is -

The equation of the line cutting an intercept of 3 units on negative y-axis and inclined at an angle tan-1 3/5 to the x-axis is -

The equation of a straight line which passes through the point (-3, 5) such that the portion of it between the axes is divided by the point in the ratio 5 : 3, internally (reckoning from x-axis) will ...

The co-ordinates of the vertices P, Q, R & S of square PQRS inscribed in the triangle ABC with vertices A ≡ (0, 0), B (3, 0) & C ≡ (2, 1) given that two of its vertices P, Q are on the sid...

The equation of perpendicular bisector of the line segment joining the points (1, 2) and (-2, 0) is -

The number of possible straight lines, passing through (2, 3) and forming a triangle with coordinate axes, whose area is 12 sq. units, is -

Points A & B are in the first quadrant ; point ′O′ is the origin. If the slope of OA is 1, slope of OB is 7 and OA = OB, then the slope of AB is -...

The line 3x + 2y = 6 will divide the quadrilateral formed by the lines x + y = 5, y - 2x = 8, 3y + 2x = 0 & 4y - x = 0 in

If the point (a, 2) lies between the lines x - y - 1 = 0 and 2(x - y) - 5 = 0, then the set of values of a is -

A(x1, y1), B(x2, y2) and C (x3, y3) are three non-collinear points in cartesian plane. Number of parallelograms that can be drawn with these three points as vertices is -...

If P = (1, 0) ; Q = (-1, 0) & R = (2, 0) are three given points, then the locus of the points S satisfying the relation, SQ2 + SR2 = 2 SP2 is...