(1) Find the distance between the following pairs of points:
(i) (2 , 3) (4 , 1) Solution
(ii) (-5 , 7) (-1 , 3) Solution
(iii) (a , b) (-a , -b) Solution
(2) Find the distance between the points (0, 0) and (36, 15). Solution
(3) Determine if the points (1,5) (2,3) and (-2,-11) are collinear. Solution
(4) Check whether (5,-2) (6,4) and (7,-2) are the vertices of an isosceles triangle. Solution
(5) In a classroom 4 friends are seated at the points A, B, C and D as shown in figure. Champa and Chameli walk into the class and after observing for a few minutes champa asks Chameli,"Don't you think ABCD is a square?" Chameli disagrees. Using distance formula, find which of them is correct.
(6) Name the type of quadrilateral formed. If any,by the following points,and give reasons for your answer:
(i) (-1, -2) (1, 0) (-1, 2) (-3, 0) Solution
(ii) (-3, 5) (3, 1) (0, 3) (-1, -4) Solution
(iii) (4, 5) (7, 6) (4, 3) (1, 2) Solution
(7) Find the points on the x-axis which is equidistant from (2, -5) and (-2, 9) Solution
(8) Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units. Solution
(9) If Q(0, 1) is equidistant from P(5, -3) and R(x, 6),find the values of x. Also find the distances QR and PR.
(10) Find a relation between x and y such that the points (x, y) is equidistant from the points (3, 6) and (-3, 4).
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