Show that the points (7,10), (-2,5) and (3,-4) are the vertices of an isosceles right triangle.

3

(a)

Show that points A(7,5),B(2,3) and C(6,-7) are the vertices of a right triangle. Also find its area.

3

(a)

Point P divides the line segment joining the points A(2,1) and B(5,-8) such that \({AP\over AB}={1\over 3}\). If P lies on the 2x-y+k=0, find the value of k.

3

(a)

The line segment AB joining the points A(3,-4) and B(1,2) is trisected at the points P(p,-2) and Q(5/3,q). Find the values of p and q.

3

(a)

If R(x,y) is a point on the line segment joining the points P(a,b) and Q(b,a) then prove that x+y=a+b

3

(a)

Find the area of the triangle whose sides are along the lines x=2, y=0 and 4x+5y=20

3

(a)

Check whether the points (3, 8), (5, 4) and (1, 2) are collinear?

3

(a)

Determine, by distance formula, whether the points (7, 10), (-2, 5) and (3, -4) are collinear?

3

(a)

Determine, whether the triangle whose vertices are given is isosceles: (10, -18), (3, 6) and (-5, 2).

3

(a)

An equilateral triangle has two vertices at the points (1, 1) and (-1, -1). Find the coordinates of the third vertex.

3

(a)

Name the figure, you will get by joining the coordinates of the points (-3, -1), (-2, 0), (-1, -1), (-1, -2) and (-3, -2).

3

(a)

The points P(2, 0), Q(9, 1), R(11, 6) and S(4, 4) are the vertices of a quadrilateral PQRS. Determine whether PQRS is a rhombus or not.

3

(a)

Show that the points A(1,0), B(5,3), C(2,7) and D(-2,4) are the vertices of a parallelogram.

3

(a)

If the point A(0,2) is equidistant from the points B(3,p) and C(p,5), find p. Also find the length of AB.

3

(a)

Points P,Q,R and S divide the line segment joining the points A(1,2) and B(6,7) in 5 equal parts. Find the coordinates of the points P,Q and R.

3

(a)