The three vertices of a parallelogram ABCD are A(3,-4), B(-1,-3) and C(-6,2). Find the coordinates of vertex D and find the area of ABCD.

4

(a)

In \(\Delta PAB, \) PA=PB and area of \(\Delta PAB=10\)sq.units. Find the coordinates of P if coordinates of A and B are (1,2) and (3,8) respectively.

4

(a)

A(0,3), B(-1,-2) and C(4,2) are vertices of a \(\Delta ABC\). D is a point on the side BC such that \({BD\over DC}={1\over2}\). P is a point on AD such that \(AP={2\sqrt5\over3}\)units. Find coordinates of P.

4

(a)

If A(-3,5), B(-2,-7), C(1,-8) and D(6,3) are the vertices of a quadrilateral ABCD, find its area.

4

(a)

Find the values of k so that the area of the triangle with vertices (1,-1), (-4,2k) and (-k,-5) in 24sq.units.

4

(a)

Prove that the area of a triangle with vertices (t,t-2), (t+2,t+2) and (t+3,t) is independent of t.

4

(a)

Find the points of trisection of the line segment determined by (7,5) and (16,-1).

4

(a)

If the points P(0,k), Q(8,3), R(6,7) and S(-2,3) are the vertices of a rectangle, taken in order, find the value of k.

4

(a)

Find the area of the triangle formed by the points P(-1.5,3), Q(6,-2) and R(-3,4).

4

(a)

Prove that the points A(2,3), B(-2,2), C(-1,-2) and D(3,-1) are the vertices of a square ABCD.

4

(a)

If P(x,y) is any point on the line segment joining the points A(a,0) and B(0,b), then show that \(\frac { x }{ a } +\frac { y }{ b } =1\)

4

(a)

Find the area of the triangle ABC with A(1,-4) and the mid-points of sides through A being (2,-1) and (0,-1).

4

(a)

The vertices of \(\Delta \)ABC are A (-2,0). B(2,0) and C (0,2) and that of \(\Delta \)PQR are P (-4,0). Q (4,0)and R (0,4).Verify that the ratio of the areas of the two triangles is equal to the square of the ratio of their corresponding sides.

4

(a)

Show that the points (4,2), (7,5) and (9,7) do not form a triangle.

4

(a)

If the points (7,-2), (5,1) and (3,k) are collinear, then find the value of k

4

(a)