EXERCISE 7.1 Question 1. Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b) Question 2. Find the distance between the points...

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EXERCISE 7.1 Question 1. Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b) 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. Question 3. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear. Question 4. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle. Question 5. 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 distance formula, find which of them is correct. Question 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) (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) (iii) (4, 5), (7, 6), (4, 3), (1, 2) Question 7. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9). Question 8. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units Question 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. Question 10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4). EXERCISE 7.2 Question 1. Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3. Question 2. Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3). Question 3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs 1 4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1 5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Answered Same DayDec 25, 2021

Answer To: EXERCISE 7.1 Question 1. Find the distance between the following pairs of points : (i) (2, 3), (4,...

David answered on Dec 25 2021
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Chapter_7_Coordinate_Geometry

Class X Chapter 7 – Coordinate Geometry Maths
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Exercise 7.1
Question 1:
Find the distance between the following pairs of points:
(i) (2, 3), (4, 1) (ii) (−5, 7), (−1, 3) (iii) (a, b), (− a, − b)
Answer:
(i) Distance between the two points is given by
(ii) Distance between is given by
(iii) Distance between is given by
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.
Answer:
Distance between points

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Class X Chapter 7 – Coordinate Geometry Maths
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Yes, we can find the distance between the given towns A and B.
Assume town A at origin point (0, 0).
Therefore, town B will be at point (36, 15) with respect to town A.
And hence, as calculated above, the distance between town A and B will be
39 km.
Question 3:
Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.
Answer:
Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C
of the given triangle respectively.
Let
Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.
Question 4:
Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.
Answer:
Let the points (5, −2), (6, 4), and (7, −2) are representing the vertices A, B, and C
of the given triangle respectively.
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Class X Chapter 7 – Coordinate Geometry Maths
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As two sides are equal in length, therefore, ABCis an isosceles triangle.
Question 5:
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the
following 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.
Answer:
It can be observed that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of
these 4 friends.
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Class X Chapter 7 – Coordinate Geometry Maths
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It can be observed that all sides of this quadrilateral ABCD are of the same length
and also the diagonals are of the same length.
Therefore, ABCD is a square and hence, Champa was correct
Question 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)
(ii) (− 3, 5), (3, 1), (0, 3), (− 1, − 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
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Answer:
(i) Let the points (−1, −2), (1, 0), (−1, 2), and (−3, 0) be representing the vertices
A, B, C, and D of the given quadrilateral respectively.
It can be observed that all sides of this quadrilateral are of the same length and also,
the diagonals are of the same length. Therefore, the given points are the vertices of
a square.
(ii)Let the points (− 3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices
A, B, C, and D of the given quadrilateral respectively.
It can be observed that all sides of this quadrilateral are of different lengths.
Therefore, it can be said that it is only a general quadrilateral, and not specific such
as square, rectangle, etc.
(iii)Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B,
C, and D of the given quadrilateral respectively.
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Class X Chapter 7 – Coordinate Geometry Maths
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It can be observed that opposite sides of this quadrilateral are of the same length.
However, the diagonals are of different lengths. Therefore, the given points are the
vertices of a parallelogram.
Question 7:
Find the point on the x-axis which is equidistant from (2, − 5) and (− 2, 9).
Answer:
We have to find a point on x-axis. Therefore, its y-coordinate will be 0.
Let the point on x-axis be .
By the given condition, these distances are equal in measure.
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Class X Chapter 7 – Coordinate Geometry Maths
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Therefore, the point is (− 7, 0).
Question 8:
Find the values of y for which the distance between the points P (2, − 3) and Q (10,
y) is 10 units.
Answer:
It is given that the distance between (2, −3) and (10, y) is 10.
Question 9:
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find
the distance QR and PR.
Answer:
Therefore, point R is (4, 6) or (−4, 6).
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Class X Chapter 7 – Coordinate Geometry Maths
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When point R is (4, 6),
When point R is (−4, 6),
Question 10:
Find a relation between x and y such that the point (x, y) is equidistant from the
point (3, 6) and (− 3, 4).
Answer:
Point (x, y) is equidistant from (3, 6) and (−3, 4).
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Exercise 7.2
Question 1:
Find the coordinates of the point which divides the join of (− 1, 7) and (4, − 3) in
the ratio 2:3.
Answer:
Let P(x, y) be the required point. Using the section formula, we obtain
Therefore, the point is (1, 3).
Question 2:
Find the coordinates of the points of trisection of the line segment joining (4, − 1)
and (− 2, − 3).
Answer:
Let P (x1, y1) and Q (x2, y2) are the points of trisection of the line segment joining
the given points i.e., AP = PQ = QB
Therefore, point P divides AB internally in the ratio 1:2.
Point Q divides AB internally in the ratio 2:1.
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Class X Chapter 7 – Coordinate Geometry Maths
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