(1) Find the mid-points of the line segment joining the points
(i) (−2, 3) and (−6,−5)
(ii) (8,−2) and (−8,0)
(iii) (a, b) and (a + 2b, 2a - b)
(iv) (1/2, -3/7) and (3/2, -11/7) Solution
(2) The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7), then find the other end
(3) If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0 , then what will be the value of p?
(4) The mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle. Solution
(5) O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8,6) and (10,0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD. Solution
(6) The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square. Solution
(7) The points A(−3, 6) , B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram
(8) A (−3, 2) , B (3, 2) and C (−3, −2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.
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