Chapter 7 · Coordinate Geometry

NCERT Class 10 Maths Exercise 7.1

All 10 questions of NCERT Class 10 Maths Exercise 7.1 (Coordinate Geometry), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Find ​the distance between the ​following ​pairs of ​points:

   1. (i)(2,3), ​(4,1)
   2. (ii)(-5,7), (-1,3)
   3. (iii)(a,b), (-a,-b).
   Show answer

   (i) $2\sqrt{2}$; (ii) $4\sqrt{2}$; (iii) $2\sqrt{a^2+b^2}$.

   Step-by-step solution →
2. Q2
   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?
   Show answer

   Distance $=39$ units, so towns A and B are $39$ km apart.

   Step-by-step solution →
3. Q3
   Determine ​if ​the points (1, ​5), (2, ​3) and ​(-2, ​-11) are collinear.
   Show answer

   The points are **not** collinear (area of $△ABC=11\ne 0$).

   Step-by-step solution →
4. Q4
   Check whether (5, -2), (6, ​4) and (7, ​-2) are ​the ​vertices ​of an isosceles triangle.
   Show answer

   Yes — the points form an isosceles triangle with $AB=BC=\sqrt{37}$ and $CA=2$.

   Step-by-step solution →
5. Q5
   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.

   Show answer

   All four sides equal $\sqrt{18}$ and both diagonals equal $6$, so $ABCD$ is a square. Champa is correct.

   Step-by-step solution →
6. Q6
   Name the ​type of ​quadrilateral formed, if any, by ​the following points, and ​give reasons for your ​answer: ​

   1. (i)$(-1,-2),(1,0),(-1,2),(-3,0)$; ​
   2. (ii)$(-3,5),(3,1),(0,3),(-1,-4)$;
   3. (iii)$(4,5),(7,6),(4,3),(1,2)$.
   Show answer

   (i) Square; (ii) No quadrilateral (three points are collinear); (iii) Parallelogram.

   Step-by-step solution →
7. Q7
   Find the ​point ​on the $x$-axis ​which is ​equidistant from $(2,-5)$ ​and $(-2,9)$.
   Show answer

   The required point is $(-7,0)$.

   Step-by-step solution →
8. Q8
   Find the values ​of $y$ ​for ​which the ​distance ​between the points $P(2,-3)$ ​and $Q(10,y)$ is $10$ ​units.
   Show answer

   $y=3$ or $y=-9$.

   Step-by-step solution →
9. Q9
   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.
   Show answer

   $x=4$ or $x=-4$; $QR=\sqrt{41}$; $PR=\sqrt{82}$ (for $x=4$) or $9\sqrt{2}$ (for $x=-4$).

   Step-by-step solution →
10. Q10
    Find ​a relation between $x$ ​and $y$ such ​that ​the point $(x,y)$ is equidistant ​from ​the point $(3,6)$ ​and $(-3,4)$.
    Show answer

    The required relation is $3x+y=5$ (equivalently $3x+y-5=0$).

    Step-by-step solution →