Find the distance between the following pairs of points:
(i) \(2\sqrt{2}\)
(ii) \(4\sqrt{2}\)
(iii) \(2\sqrt{a^2 + b^2}\)
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?
39; 39 km
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
No
Check whether (5, −2), (6, 4) and (7, −2) are the vertices of an isosceles triangle.
Yes
In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. 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 the distance formula, find which of them is correct.
Champa is correct.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) Square
(ii) No quadrilateral
(iii) Parallelogram
Find the point on the x-axis which is equidistant from (2, −5) and (−2, 9).
(−7, 0)
Find the values of y for which the distance between the points P(2, −3) and Q(10, y) is 10 units.
−9, 3
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.
x = ±4
QR = \(\sqrt{41}\)
PR = \(\sqrt{82}, 9\sqrt{2}\)
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).
\(3x + y - 5 = 0\)