Class 10 Maths · Chapter 7

Coordinate Geometry

440 Class 10 Maths questions on Coordinate Geometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 18 of 22

1. Q341 CBSE 2020
   Seema has a $10$ m $\times$ $10$ m kitchen garden attached to her kitchen. She divides it into a $10\times 10$ grid and wants to grow some vegetables and herbs used ​in the kitchen. She puts some soil and manure ​in that and sows a green chilly plant at $A$, ​a coriander plant at $B$ ​and a tomato plant at $C$. Her friend Kusum visited the garden ​and praised the plants grown there. She pointed out that ​they seem to be in a straight line. See the ​below ​diagram carefully and answer the following questions :

   1. (i)Write the coordinates of the points $A$, $B$ and $C$ taking the $10\times 10$ grid as coordinate axes.
   2. (ii)By distance formula or some other formula, check whether the points are collinear.
   Show answer

   (i) $A(2,2)$, $B(5,4)$, $C(7,6)$. (ii) $AB+BC=\sqrt{13}+2\sqrt{2}\approx 6.43\ne \sqrt{41}=AC$ (area of $△ABC=1\ne 0$), so $A$, $B$, $C$ are **not** collinear.

   Step-by-step solution →
2. Q342 CBSE 2020
   Find the co-ordinates of the ​points of trisection ​of the ​line segment ​joining ​the ​points $(3,-1)$ ​and $(6,8)$.
   Show answer

   The points of trisection are $(4,2)$ and $(5,5)$.

   Step-by-step solution →
3. Q343 CBSE 2020
   Find ​the ratio ​in which ​the $y$-axis divides the ​line segment joining the ​points $(6,-4)$ ​and $(-2,-7)$. Also find ​the point of intersection.
   Show answer

   The y-axis divides the segment in the ratio $3:1$, and the point of intersection is $\left(0,-\frac{25}{4}\right)$.

   Step-by-step solution →
4. Q344 CBSE 2020
   Find the ​area ​of a quadrilateral $ABCD$ ​having ​vertices ​at $A(1,2)$, $B(1,0)$, $C(4,0)$ ​and $D(4,4)$.
   Show answer

   Area of quadrilateral $ABCD=9$ square units.

   Step-by-step solution →
5. Q345 CBSE 2020
   Show that ​the points $(7,10)$, $(-2,5)$ ​and $(3,-4)$ are vertices ​of an isosceles ​right ​triangle.
   Show answer

   $PQ=QR=\sqrt{106}$ and $P{Q}^2+Q{R}^2=212=P{R}^2$, so $△PQR$ is an isosceles right triangle, right-angled at $Q$.

   Step-by-step solution →
6. Q346 CBSE 2020
   If points $A(0,3)$, $B(-2,a)$ and $C(-1,4)$ are the ​vertices of a right triangle right-angled at $A$, then

   1. (i)​find the value ​of '$a$', ​
   2. (ii)find the length of the ​longest ​side, and
   3. (iii)find the area ​of $△ABC$.
   Show answer

   $a=1$; the longest side is $BC=\sqrt{10}$ units; the area of $△ABC$ is $2$ square units.

   Step-by-step solution →
7. Q347 CBSE 2020
   In ​what ​ratio does ​the point $P(-4,y)$ ​divide the line ​segment joining the points $A(-6,10)$ and $B(3,-8)$ if it lies on $AB$. Hence ​find the ​value of $y$.
   Show answer

   $P$ divides $AB$ in the ratio $2:7$, and $y=6$.

   Step-by-step solution →
8. Q348 CBSE 2020
   Find ​the area of ​triangle $PQR$ ​formed ​by the ​points $P(-5,7)$, $Q(-4,-5)$ ​and $R(4,5)$.
   Show answer

   Area $=53$ square units

   Step-by-step solution →
9. Q349 CBSE 2020
   If the point $C(-1,2)$ divides internally ​the line ​segment joining $A(2,5)$ and $B(x,y)$ ​in the ​ratio $3:4$, ​find the coordinates ​of $B$.
   Show answer

   $B=(-5,-2)$.

   Step-by-step solution →
10. Q350 CBSE 2020
    Find ​the ​area of triangle $ABC$ with $A(1,-4)$ ​and the ​mid-points of sides through $A$ ​being $(2,-1)$ and $(0,-1)$.
    Show answer

    Area of $△ABC=12$ square units.

    Step-by-step solution →
11. Q351 CBSE 2020
    The coordinates of the mid-point P of ​the ​line ​segment joining the points $A(3p,4)$ and $B(-2,2q)$ are $(5,p)$. ​Find ​the ​values of $p$ ​and $q$.
    Show answer

    $p=4$ and $q=2$.

    Step-by-step solution →
12. Q352 CBSE 2020
    In a classroom, ​4 ​friends are seated at the points A, B, C and D as shown in ​Fig. 3. 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 sides $=3\sqrt{2}$ and both diagonals $=6$, so ABCD is a square — Champa is correct.

    Step-by-step solution →
13. Q353 CBSE 2020
    To conduct ​Sports Day ​activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from ​each other along AD, as shown in Fig. 5. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line ​and posts a green flag. ​Preet runs $\frac{1}{5}$ th the distance AD on the eighth line ​and posts a ​red ​flag.

    1. (i)What is the distance between the two flags?[1]
    2. (ii)If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post the blue flag?[2]
    Show answer

    (i) Distance between the flags $=\sqrt{61}\approx 7.81$ m. (ii) The blue flag should be at $(5,22.5)$, i.e. on the 5th line, $22.5$ m up AD.

    Step-by-step solution →
14. Q354 CBSE 2020
    In Fig. 3, ​arrangement ​of desks ​in a classroom is shown. Ashima, Bharti and Asha are seated ​at $A$, $B$ and $C$ respectively. Answer ​the following :

    1. (i)​Find whether ​the girls are sitting in a line.
    2. (ii)If $A$, $B$ and $C$ are collinear, find the ratio in ​which point $B$ divides the line segment joining $A$ and $C$.

    Show answer

    (i) Yes — $A$, $B$, $C$ are collinear (the girls are sitting in a line). (ii) $B$ divides $AC$ in the ratio $3:2$.

    Step-by-step solution →
15. Q355 CBSE 2019
    Find the coordinates of a point $A$, ​where $AB$ is ​diameter of a ​circle whose centre is $(2,-3)$ and $B$ is ​the ​point $(1,4)$.
    Show answer

    $A=(3,-10)$

    Step-by-step solution →
16. Q356 CBSE 2019
    Find ​the ​distance between ​the ​points $(a,b)$ and $(-a,-b)$.
    Show answer

    The distance is $2\sqrt{a^2+b^2}$.

    Step-by-step solution →
17. Q357 CBSE 2019
    If $P(4,y)$ is ​the ​mid-point ​of ​the line-segment joining ​the points $A(3,-2)$ and $B(5,2)$, ​find the ​value of $y$.
    Show answer

    $y=0$.

    Step-by-step solution →
18. Q358 CBSE 2019
    Find the ​value(s) ​of $x$, ​if ​the distance between the ​points $A(0,0)$ and $B(x,-4)$ is $5$ units.
    Show answer

    $x=3$ or $x=-3$.

    Step-by-step solution →
19. Q359 CBSE 2019
    Write the coordinates ​of ​a point $P$ on $x$-axis ​which ​is equidistant ​from the ​points $A(-2,0)$ ​and $B(6,0)$.
    Show answer

    $P=(2,0)$.

    Step-by-step solution →
20. Q360 CBSE 2019
    Points $A(3,1)$, $B(5,1)$, $C(a,b)$ ​and $D(4,3)$ ​are ​vertices of a ​parallelogram $ABCD$. Find the ​values of $a$ ​and $b$.
    Show answer

    $a=6$ and $b=3$, so $C(6,3)$

    Step-by-step solution →