Coordinate Geometry (10)

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If the points A(2, 3), B(-5, 6), C(6, 7) and D(p, 4) are the vertices of a parallelogram ABCD, find the value of p.

Find the coordinates of the point which divides the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.

If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD. 

If A(-2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence find m.

Find the distance of a point P(x, y) from the origin.

In what ratio does the point (24/11, y) divide the line segment joining the points P(2, -2) and Q(3, 7) ? Also find the value of y.

If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y. 

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and

Find the ratio in which the line x - 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of

Find the area of a triangle whose vertices are given as (1, -1) (-4, 6) and (-3, -5). 

Find a relation between x and y if the points A(x, y), B(-4, 6) and C(-2, 3) are collinear

Write the coordinates of a point P on x-axis which is equidistant from the points A(-2, 0) and B(6, 0).