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Solution of Exercise 7.1 (NCERT)

Question: 1 - Find the distance between the following pairs of points:
Solution of coordinate geometry 1NCERT Exercise 7.1
Solution of coordinate geometry 2NCERT Exercise 7.1
Solution of coordinate geometry 3NCERT Exercise 7.1

Question: 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.
Solution:
In particular, the distance of a point (x, y) from the origin is given by
Solution of coordinate geometry 4NCERT Exercise 7.1
Now, as discussed in Section 7.2 in the book, town B is 36 east and 15 north from the town A. Thus, distance between town A and B will be equal to 39 unit. If distance is measured in km, then distance will be equal to 39 km.
Question: 3 – Determine if the points (1, 5), (2, 3) and (–2, –11) are collinear.
Solution:
Solution of coordinate geometry 5NCERT Exercise 7.1
Thus, distance between AB by distance formula
Solution of coordinate geometry 6NCERT Exercise 7.1
Now, distance between BC by distance formula
Solution of coordinate geometry 7NCERT Exercise 7.1
And distance between AC by distance formula
Solution of coordinate geometry 8NCERT Exercise 7.1
Thus, given points are non-collinear.

Question: 4 – Check whether (5, 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution of coordinate geometry 9NCERT Exercise 7.1
Solution of coordinate geometry 10NCERT Exercise 7.1
Thus, given triangle is an isosceles triangle.
Question: 5 – In a classroom, 4 friends are seated at the points A, B, C and D as shown in Figure 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa as Chameli, “Don’t you think ABCD is square?” Chameli disagrees. Using distance formula find which of them is correct.
Solution:
Here, coordirantes are A (3, 4), B (6, 7), C (9, 4) and D (6, 1)
Solution of coordinate geometry 11NCERT Exercise 7.1
Solution of coordinate geometry 12NCERT Exercise 7.1
Solution of coordinate geometry 13NCERT Exercise 7.1
Since, all four sides are equal and diagonals are also equal thus, it is clear that ABCD is a square and hence, Champa is right.
Question: 6 – Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
Solution of coordinate geometry 14NCERT Exercise 7.1
Solution of coordinate geometry 15NCERT Exercise 7.1
Solution of coordinate geometry 16NCERT Exercise 7.1
Solution of coordinate geometry 17NCERT Exercise 7.1
Thus, ABCD is a square.
Solution of coordinate geometry 18NCERT Exercise 7.1
Solution of coordinate geometry 19NCERT Exercise 7.1
Since, sides are not equal, thus only a general and not a specific quadrilateral such as square or parallelogram is formed.
Solution of coordinate geometry 20NCERT Exercise 7.1
Solution of coordinate geometry 21NCERT Exercise 7.1
Solution of coordinate geometry 22NCERT Exercise 7.1
Here opposite sides are equal but diagonals are not equal, thus with the given points a parallelogram is formed.

Question: 7 – Find the point on the axis which is equidistant from (2, –5) and (– 2, 9).
Solution:
Let given coordinates are A(2, –5), BC (–2, 9) and P(x, 0) is on the x-axis.
Since, the third coordinate is at equidistance from the given coordinates, thus AP = BP
Solution of coordinate geometry 23NCERT Exercise 7.1
Solution of coordinate geometry 24NCERT Exercise 7.1
Question: 8 – Find the value of y for the distance between the points P(2, – 3) and Q (10, y) is 10 units.
Solution:
Given, P(2, –3) and Q(10, y) and QP = 10 unit
Solution of coordinate geometry 25NCERT Exercise 7.1
Solution of coordinate geometry 26NCERT Exercise 7.1
Thus, required value = 3 or – 9

Question: 9 – If Q (0, 1) is equidistant from P(5, – 3) and R (x, 6), find the value of x. Also find the distances QR and PR.
Solution:
Given, Q(0, 1), P(5, –3) and R(x, 6) and QP = QR
Solution of coordinate geometry 27NCERT Exercise 7.1
Solution of coordinate geometry 28NCERT Exercise 7.1
Solution of coordinate geometry 29NCERT Exercise 7.1
Solution of coordinate geometry 30NCERT Exercise 7.1
Question: 10 – Find the relation between x and y such that the point (x, y) is equidistance from the point (3, 6) and (–3, 4).
Solution:
Let P(x, y), A (3, 6) and B (– 3, 4)
Here AP = BP
Solution of coordinate geometry 31NCERT Exercise 7.1
Solution of coordinate geometry 32NCERT Exercise 7.1

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