Math- Coordinate Geometry Set 1

The vertices of a triangle are (0, 0), (3, 0) and (0, 4). The centroid of the triangle is

The area (in square units) of the triangle formed by the points A(a, 0), 0(0, 0) and B(0, b) is

The area of the triangle with vertices at the points (a, b + c), (b, c + a) and (c, a + b) is

The points (k + 1, 1), (2k + 1, 3) and (2k + 2, 2k) are collinear if

The point P which divides the line segment joining the points A(2, -5) and B(5, 2) in the ratio 2 : 3 lies in the quadrant

If P(l, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then

If p[latex]\left(\frac{a}{3}, 4\right)[/latex] is the mid-point of the line segment joining the points Q (-6, 5) and R (-2, 3), then the value of a is

If the distance between the points (4, p) and (1, 0) is 5 units, then the value of p is 

The perimeter of a triangle with vertices (0,4), (0, 0) and (3, 0) is