90. A is a point on the y-axis who’s ordinate is 5 and B is the point (3, 1). Calculate the length of AB.
91. The mid point of the line segment joining (2a, 4) and (2, 3b) is (1, 2a +1). Find the values of a and Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle.
92. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by they-axis? Also, find the coordinates of the point of division.
93. Show that the points A (1, 2), B(S, 4), C(3, 8) and D(— 1,6) are the vertices of a square.
94. Find the co-ordinates of the point equidistant from three given points A (5, 1), B (- 3, -7) and C (7, -1).
95. Find the value of p for which the point (-1, 3), (2, p) and (5, -1) are collinear.
96. If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b.
97. Prove that the points (-4, -1); (-2, -4); (4, 0) and (2, 3) are vertices of a rectangle.
98. The vertices of a triangle are (—1, 3); (1, —1) and (5, 1). Find the lengths of medians through vertices (—1, 3) and (5, 1).
99. Show that the points A (2, -2), B (14, 10), C (11, 13) and D (-1, 1) are the vertices of a rectangle.
100. Determine the ratio in which the points (6, a) divides the join of A (-3, -1) and B (-8, 9). Also find the value of “a”.
91. The mid point of the line segment joining (2a, 4) and (2, 3b) is (1, 2a +1). Find the values of a and Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle.
92. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by they-axis? Also, find the coordinates of the point of division.
93. Show that the points A (1, 2), B(S, 4), C(3, 8) and D(— 1,6) are the vertices of a square.
94. Find the co-ordinates of the point equidistant from three given points A (5, 1), B (- 3, -7) and C (7, -1).
95. Find the value of p for which the point (-1, 3), (2, p) and (5, -1) are collinear.
96. If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b.
97. Prove that the points (-4, -1); (-2, -4); (4, 0) and (2, 3) are vertices of a rectangle.
98. The vertices of a triangle are (—1, 3); (1, —1) and (5, 1). Find the lengths of medians through vertices (—1, 3) and (5, 1).
99. Show that the points A (2, -2), B (14, 10), C (11, 13) and D (-1, 1) are the vertices of a rectangle.
100. Determine the ratio in which the points (6, a) divides the join of A (-3, -1) and B (-8, 9). Also find the value of “a”.
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