Chapter 7 · Coordinate Geometry

NCERT Exemplar Class 10 Maths Exercise 7.1

All 20 questions of NCERT Exemplar 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
   The distance ​of ​the point $P(2,3)$ from ​the $x$-axis ​is

   1. (a)$2$
   2. (b)$3$
   3. (c)$1$
   4. (d)$5$
   Show answer

   (b) $3$

   Step-by-step solution →
2. Q2
   The ​distance between ​the points $A(0,6)$ and $B(0,-2)$ ​is

   1. (a)6
   2. (b)8
   3. (c)4
   4. (d)2
   Show answer

   (b) 8

   Step-by-step solution →
3. Q3
   The ​distance of ​the ​point $P(-6,8)$ from ​the ​origin is

   1. (a)8
   2. (b)$2\sqrt{7}$
   3. (c)10
   4. (d)6
   Show answer

   (c) 10

   Step-by-step solution →
4. Q4
   The ​distance ​between ​the ​points $(0,5)$ and $(-5,0)$ is

   1. (a)$5$
   2. (b)$5\sqrt{2}$
   3. (c)$2\sqrt{5}$
   4. (d)$10$
   Show answer

   (b) $5\sqrt{2}$

   Step-by-step solution →
5. Q5
   AOBC ​is a rectangle whose three vertices ​are vertices $A(0,3)$, $O(0,0)$ and $B(5,0)$. The length ​of ​its ​diagonal ​is

   1. (a)5
   2. (b)3
   3. (c)$\sqrt{34}$
   4. (d)4
   Show answer

   (c) $\sqrt{34}$

   Step-by-step solution →
6. Q6
   The ​perimeter of a triangle ​with ​vertices $(0,4)$, $(0,0)$ ​and $(3,0)$ is

   1. (a)$5$
   2. (b)$12$
   3. (c)$11$
   4. (d)$7+\sqrt{5}$
   Show answer

   (b) $12$

   Step-by-step solution →
7. Q7
   The area ​of ​a ​triangle ​with vertices $A(3,0)$, $B(7,0)$ ​and $C(8,4)$ is

   1. (a)$14$
   2. (b)$28$
   3. (c)$8$
   4. (d)$6$
   Show answer

   (c) $8$

   Step-by-step solution →
8. Q8
   The ​points $(-4,0)$, $(4,0)$, $(0,3)$ ​are the ​vertices of ​a

   1. (a)right triangle
   2. (b)isosceles triangle
   3. (c)equilateral triangle
   4. (d)scalene triangle
   Show answer

   (b) isosceles triangle

   Step-by-step solution →
9. Q9
   The point which divides the ​line segment ​joining ​the points $(7,-6)$ and $(3,4)$ ​in ​ratio $1:2$ ​internally lies ​in the

   1. (a)I quadrant
   2. (b)II quadrant
   3. (c)III quadrant
   4. (d)IV quadrant
   Show answer

   (d) IV quadrant

   Step-by-step solution →
10. Q10
    The point which ​lies ​on the perpendicular ​bisector ​of ​the line ​segment joining the ​points $A(-2,-5)$ and $B(2,5)$ is

    1. (a)$(0,0)$
    2. (b)$(0,2)$
    3. (c)$(2,0)$
    4. (d)$(-2,0)$
    Show answer

    (a) $(0,0)$

    Step-by-step solution →
11. Q11
    The fourth ​vertex ​D ​of ​a ​parallelogram ​ABCD whose three vertices are $A(-2,3)$, $B(6,7)$ and $C(8,3)$ ​is

    1. (a)$(0,1)$
    2. (b)$(0,-1)$
    3. (c)$(-1,0)$
    4. (d)$(1,0)$
    Show answer

    (b) $(0,-1)$

    Step-by-step solution →
12. Q12
    If ​the point $P(2,1)$ lies on the ​line ​segment ​joining points $A(4,2)$ and $B(8,4)$, then

    1. (a)$AP=\frac{1}{3}AB$
    2. (b)$AP=PB$
    3. (c)$PB=\frac{1}{3}AB$
    4. (d)$AP=\frac{1}{2}AB$
    Show answer

    (d) $AP=\frac{1}{2}AB$

    Step-by-step solution →
13. Q13
    If $P\left(\frac{a}{3},4\right)$ ​is the mid-point of the line ​segment joining ​the ​points $Q(-6,5)$ and $R(-2,3)$, then the ​value of $a$ ​is

    1. (a)$-4$
    2. (b)$-12$
    3. (c)$12$
    4. (d)$-6$
    Show answer

    (b) $-12$

    Step-by-step solution →
14. Q14
    The ​perpendicular bisector of ​the ​line segment joining ​the points ​A $(1,5)$ ​and B $(4,6)$ ​cuts the $y$-axis ​at

    1. (a)$(0,13)$
    2. (b)$(0,-13)$
    3. (c)$(0,12)$
    4. (d)$(13,0)$
    Show answer

    (a) $(0,13)$

    Step-by-step solution →
15. Q15
    The coordinates of the point which is equidistant ​from the ​three vertices of the $△AOB$ ​as ​shown ​in Fig. 7.1 is

    1. (a)$(x,y)$
    2. (b)$(y,x)$
    3. (c)$\left(\frac{x}{2},\frac{y}{2}\right)$
    4. (d)$\left(\frac{y}{2},\frac{x}{2}\right)$
    Show answer

    (a) $(x,y)$

    Step-by-step solution →
16. Q16
    A ​circle drawn with origin as the ​centre passes through $\left(\frac{13}{2},0\right)$. The point which does ​not ​lie in the ​interior of ​the ​circle ​is

    1. (a)$\left(-\frac{3}{4},1\right)$
    2. (b)$\left(2,\frac{7}{3}\right)$
    3. (c)$\left(5,-\frac{1}{2}\right)$
    4. (d)$\left(-6,\frac{5}{2}\right)$
    Show answer

    (d) $\left(-6,\frac{5}{2}\right)$

    Step-by-step solution →
17. Q17
    A line ​intersects ​the y-axis and x-axis at the points P and Q, respectively. If $(2,-5)$ ​is the ​mid-point of PQ, ​then ​the coordinates of P and Q ​are, respectively

    1. (a)$(0,-5)$ and $(2,0)$
    2. (b)$(0,10)$ and $(-4,0)$
    3. (c)$(0,4)$ and $(-10,0)$
    4. (d)$(0,-10)$ and $(4,0)$
    Show answer

    (d) $(0,-10)$ and $(4,0)$

    Step-by-step solution →
18. Q18
    The ​area ​of a ​triangle ​with ​vertices $(a,b+c)$, $(b,c+a)$ ​and $(c,a+b)$ is

    1. (a)$(a+b+c{)}^2$
    2. (b)$0$
    3. (c)$a+b+c$
    4. (d)$abc$
    Show answer

    (b) $0$

    Step-by-step solution →
19. Q19
    If the distance between ​the ​points $(4,p)$ ​and $(1,0)$ is 5, then ​the ​value ​of $p$ is

    1. (a)4 only
    2. (b)$\pm 4$
    3. (c)-4 only
    4. (d)0
    Show answer

    (b) $\pm 4$

    Step-by-step solution →
20. Q20
    If ​the points $A(1,2)$, $O(0,0)$ and $C(a,b)$ ​are collinear, ​then

    1. (a)$a=b$
    2. (b)$a=2b$
    3. (c)$2a=b$
    4. (d)$a=-b$
    Show answer

    (c) $2a=b$

    Step-by-step solution →