Mathematics · Quantitative Aptitude

Coordinate Geometry

221 Questions

Practice fundamental coordinate geometry questions covering reflections, collinear points, and loci. This collection helps in mastering XY plane plots, midpoints, and quadrant identification. It is highly beneficial for students preparing for quantitative aptitude tests, JEE, and state level engineering exams.

Point reflectionCollinear pointsXY plane lociFinding midpointsCoordinate quadrantsRhombus vertices

Coordinate Geometry Questions

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Find a point on the y-axis which equidistant from the points $A(6,5)$ and $B(-4,3)$

  1. $(0,9)$
  2. $(9,0)$
  3. $(3,0)$
  4. $(4,0)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the point be (0, y). Equidistance means the square of the distances to (6,5) and (-4,3) are equal: (0-6)^2 + (y-5)^2 = (0-(-4))^2 + (y-3)^2. This simplifies to 36 + y^2 - 10y + 25 = 16 + y^2 - 6y + 9, which results in 61 - 10y = 25 - 6y, or 4y = 36, so y = 9.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The point on X-axis which is equidistant from the point (3, 5) and (4, 2)

  1. (-6, 0)

  2. (-7, 0)

  3. (7, 0)

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the point on x-axis equidistant from (3,5) and (4,2) be (x,0),


Then, Distance of point from (3,5) = DIstance of point from (4,2)
$\rightarrow \sqrt{(3-x)^2+(5-0)^2} = \sqrt{(4-x)^2+(2-0)^2}$
$\Rightarrow 9+x^2-6x+25=16+x^2-8x+4$
$\rightarrow 2x = -14$
$\rightarrow x = -7$
$\rightarrow $ Point is $(-7,0)$

Thus, B is the correct answer.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Two points $(a, 3)$ and $(5, b)$ are the opposite vertices of a rectangle. If the coordinates $(x, y)$ of the other two vertices satisfy the relation $y = 2x + c$ where $c^{2}+ 2a -b =0$ then the value $c$ can be

  1. $2\sqrt{2}+1$
  2. $2\sqrt{2}-1$
  3. $1-2\sqrt{2}$
  4. $-1-2\sqrt{2}$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Mid-point of the other vertices is also the mid-point of the given vertices and hence satisfies the given relation
So, $\cfrac { b+3 }{ 2 } =2\left( \cfrac { a+5 }{ 2 }  \right) +c$
$\Rightarrow 2a+2c-b+7=0$
Also, ${ c }^{ 2 }+2a-b=0$
$\Rightarrow { c }^{ 2 }-2c-7=0\Rightarrow c=1\pm 2\sqrt { 2 } $

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Three vertices of rhombus taken in order are $(2, -1), (3, 4)$ and $(-2, 3)$. Find the fourth vertex.

  1. $(1, 2)$
  2. $(-3, -2)$
  3. $(3, 2)$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be the mid point of one diagonal formed by (2, -1) and (-2, 3) then using mid-point method;
Coordinate of $M \left (\dfrac {2 - 2}{2}, \dfrac {-1 + 3}{2}\right ) = (0, 1)$
$\Rightarrow \left (\dfrac {x + 3}{2}, \dfrac {y + 4}{2}\right ) = (0, 1)$
$\Rightarrow x = -3$ and $y = -2$
$\therefore (-3, -2)$ is coordinate of $D$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

What is the midpoints between the coordinates $(-1, 2)$ and $(-1, -6)$?

  1. $\left(1, 2\right)$
  2. $\left(-1, 2\right)$
  3. $\left(-1, -2\right)$
  4. $\left(1, -2\right)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know the midpoint formula between two points.
$\left(\dfrac{x _{1}+x _{2}}{2},\dfrac{y _{1}+y _{2}}{2}\right)$
Substitute the values, we get
$=$ $\left(\dfrac{-1-1}{2},\dfrac{2-6}{2}\right)$
$=$ $\left(\dfrac{-2}{2},\dfrac{-4}{2}\right)$
Therefore, midpoint is $\left(-1, -2\right)$

Multiple choice maths constructions mid-point formula midpoints division of a line segment

What is the midpoints between the coordinates $(0, -6)$ and $(4, -4)$?

  1. $\left(-2, -5\right)$
  2. $\left(2, 5\right)$
  3. $\left(2, -4\right)$
  4. $\left(2, -5\right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know the midpoint formula between two points.
$\left(\dfrac{x _{1}+x _{2}}{2},\dfrac{y _{1}+y _{2}}{2}\right)$
Substitute the values, we get
$=$ $\left(\dfrac{0+4}{2},\dfrac{-6-4}{2}\right)$
$=$ $\left(\dfrac{4}{2},\dfrac{-10}{2}\right)$
Therefore, midpoint is $\left(2, -5\right)$.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Find the midpoints between the coordinates $(2, 3)$ and $(1, 0)$

  1. $\left(\dfrac{1}{2},\dfrac{3}{2}\right)$
  2. $\left(\dfrac{3}{2},\dfrac{1}{2}\right)$
  3. $\left(\dfrac{3}{2},\dfrac{4}{2}\right)$
  4. $\left(\dfrac{3}{2},\dfrac{3}{2}\right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Midpoint between the coordinates $(x _1,y _1)$ and $(x _2,y _2)$ is:

$\left( \dfrac { x _{ 1 }+x _{ 2 } }{ 2 } ,\dfrac { y _{ 1 }+y _{ 2 } }{ 2 }  \right)$
Therefore, the midpoint between the coordinates $(2,3)$ and $(1,0)$ is: 
$\left( \dfrac { 2+1 }{ 2 } ,\dfrac { 3+0 }{ 2 }  \right) =\left( \dfrac { 3 }{ 2 } ,\dfrac { 3 }{ 2 }  \right)$
Therefore, midpoint is $\left (\dfrac {3}{2}, \dfrac {3}{2}\right)$.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

A square is formed by the points $(4, 5), (12, 5), (12, -3)$ and $(4, -3)$. Find the coordinates of the point at which the diagonals of the square intersect.

  1. $(8, 5)$
  2. $(9, 6)$
  3. $(8, 1)$
  4. $(12, 1)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that the diagonal of square is intersect equal at mid point. 

Then mid point of diagonal $(4,5)$ and $(12,-3)$ is $\left ( \dfrac{12+4}{2} \right ),\left ( \dfrac{5-3}{2} \right )=\left ( \dfrac{16}{2} \right ),\left ( \dfrac{5-3}{2} \right )= (8,1)$
Then mid point of diagonal $(12,5)$ and $(14,-3)$ is $\left ( \dfrac{12+4}{2} \right ),\left ( \dfrac{5-3}{2} \right )=\left ( \dfrac{16}{2} \right ),\left ( \dfrac{5-3}{2} \right )= (8,1)$
Then diagonal intersect at point $(8,1)$.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

In the $xy$-coordinate plane, the coordinates of three vertices of a rectangle are $\left(1, 5\right)$, $\left(5, 2\right)$ and $\left(5, 5\right)$. What are the coordinates of the fourth vertex of the rectangle?

  1. $\left(1, 2\right)$
  2. $\left(1, 7\right)$
  3. $\left(2, 1\right)$
  4. $\left(2, 5\right)$
  5. $\left(5, 7\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The intersection point of diagonals of rectangle is midpoint of each diagonal.

Let the fourth coordinate be $(x,y)$. By the above property we get 
$ \dfrac { x+5 }{ 2 } =\dfrac { 1+5 }{ 2 } $. which implies $x=1$.
$\dfrac { y+5 }{ 2 } =\dfrac { 2+5 }{ 2 } $. which implies $y=2$).
So, the coordinate $(x,y)$ is $(1,2)$.

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points $(-2,-1),(1,0),(4,3)$ and $(1,2)$ meet.

  1. $(1,1)$
  2. $(1,3)$
  3. $(5,1)$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The vertices of parallelogram in order are $A(-2,-1), B(1,0), C(4,3), D(1,2)$.


So the diagonals will be $AC$ and $BD$.

Since the diagonals of a parallelogram bisects each other, so mid-point of 

$AC$ or $BD$ will be intersection point of diagonals.

Hence by mid-point theorem, mid-point of $AC$ is

$A(-2,-1) \  and \ C(4,3)$

$x=\dfrac{-2+4}{2}=1$ and $y=\dfrac{-1+3}{2}=1$.

so $(1,1)$ is required point.

Multiple choice maths linear graphs coordinates of a point plotting and reading points on a coordinate plane position and numbers

Write the quadrant in which the following point lie
$(5, -3)$

  1. $Q _4$
  2. $Q _3$
  3. $Q _2$
  4. $Q _1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
First quadrant        X=positive    and  Y=positive

Second quadrant  X=negative   and  Y=positive

Third quadrant      X=negative    and  Y=negative

Fourth quadrant    X=positive     and  Y=negative

$ (5,-3)$ has $X=5$, positive and $Y=3$,negative

$\therefore$ The point lies in the fourth quadrant.