TRIG TEST

1. Find a point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3).
2. Find the value of x for which the distance between the point P(2, -3) and Q(x, 5) is 10 units.
3. The coordinates of the vertices of triangle ABC are A(4, 1), B(-3, 2) and C(0, k). Given that the area of triangle ABC is 12 sq. unit. Find the value of k.
4. Find the co-ordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
5. If A(6, -1), B(1, 3) and C(k, 8) are three points such that AB = BC. Find the value of k.
6. Find the area of the quadrilateral whose vertices taken in order are A(-5, -3), B(-4, -6), C(2, -1) and D(1, 2)
7. For what value of ‘k’ the points A(1, 5), B(k, 1) and C(4, 11) are collinear?
8. In what ratio does the point P(2, -5) divide the line segment joining A(-3, 5) and B(4, -9)?
9. Find the ratio in which the line segment joining the points A(3, -6) and B(5, 3) is divided by x-axis. Also find the coordinates of the point of intersection.
10. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find the value of x and y.