Short Answer TypeFind the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that 
and P lies on the line segment Ab.
Long Answer TypeFind the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.
Let P, Q and R be the three points which divide the line-segment joining the points A(-2, 2) and B(2, 8) in four equal parts.
Case I. For point P, we have
Hence, m1 = 1, m2 = 3
x1 = -2, y2 = 2
x2 = 2, y2 = 8
Then, coordinates of P are given by
Case II. For point Q, we have
m1 = 2, m2 = 2
x1 = -2, y1 = 2
and x2 = 2, y2 = 8
Then, coordinates of Q are given by
Case III. For point R, we have
Hence, m1 = 3, m2 = 1
x1 = -2, y1 = 2
and x2 = 2, y2 = 8
Then co-ordinates of R are given by
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order.
Short Answer TypeIn each of the following find the value of ‘k’, for which the points are collinear
(7, –2), (5, 1), (3, k)
In each of the following find the value of ‘k’, for which the points are collinear
(8, 1), (k, – 4), (2, –5)
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Long Answer TypeFind the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3).
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