Mathematics · Quantitative Aptitude

Coordinate Geometry and Construction

139 Questions

Coordinate geometry involves finding midpoints, calculating ratios of line segments, and understanding 3D projections. These concepts are crucial for tackling quantitative aptitude sections. Practice these questions to master geometric constructions and coordinate plotting.

Midpoint calculationsSection formulas3D geometry projectionsGeometric construction stepsLine segment ratios

Coordinate Geometry and Construction Questions

Multiple choice general knowledge math & puzzles

The Midpoint Theorem states: "A line joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half the length of the third side." So, riddle me this: What is the converse of the Midpoint Theorem is it" "If a line is parallel to one side of a triangle and is equal to half the length of the same side, the given line passes through the midpoints of the other two sides." "

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The converse of the Midpoint Theorem states that a line drawn through the midpoint of one side of a triangle, parallel to another side, bisects the third side. The statement provided in the question is not the standard converse.

Multiple choice general knowledge math & puzzles

Mid point formula?

  1. (x1+x2/2,y1+y2/2)

  2. (x1+x2+y1+y2)/2

  3. (x1-x2/2,y1-y2/2)

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

The midpoint formula calculates the average of the x-coordinates and the y-coordinates: ((x1+x2)/2, (y1+y2)/2). Option 422345 is the standard representation.

Multiple choice

Consider points P and Q in the x - y plane, with P = (1, 0) and Q (0, 1). The line integral 2$\int\limits_P^o (x dx + ydy)$along the semicircle with the line segment PQ as its diameter

  1. is - 1

  2. is 0

  3. is 1

  4. depends on the direction (clockwise or anti - clockwise) of the semicircle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$I = 2 \int\limits_P^Q (xdx + ydy) \\ = 2 \int\limits_P^Q xdx + 2 \int\limits_P^Q ydy \\ = 2 \int\limits_1^0 xdx + 2 \int\limits_1^0 ydy = 0$

Multiple choice mathematics and statistics angle and its measurement directed angles

The equation to the perpendicular bisector of the line segment joining (5,7) (3,1) is 

  1. $3x+y =16$
  2. $x - 3y =12$
  3. $x+ 3y =16$
  4. $3x - y =12$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, $A=(5,7)$ and $B=(3,1)$


Here, $x _1=5,y _1=7,x _2=3$ and $y _2=1$


$\Rightarrow$  Mid-point of $A$ and $B=$ $\left(\dfrac{x _1+x _2}{2},\dfrac{y _1+y _2}{2}\right)$

                                            $=\left(\dfrac{5+3}{2},\dfrac{7+1}{2}\right)$

                                            $=\left(4,4\right)$

$\Rightarrow$  Slope of $AB\,(m)=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3$

$\Rightarrow$  Slope of the perpendicular $(m _1)$ $=\dfrac{-1}{m}=\dfrac{-1}{3}$

The perpendicular passes through $(4,4)$.

The equation is,
$\Rightarrow$  $y-4=\dfrac{-1}{3}(x-4)$

$\Rightarrow$  $3y-12=-x+4$

$\Rightarrow$  $x+3y=16$

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

When a perpendicular is drawn to a given line, in what ratio is the line divided into?

  1. $1:1$
  2. $1:2$
  3. $2:1$

  4. Cannot be said
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A line does not have a definite length.

Hence, when a perpendicular is drawn to the given line, nothing can be said about the ratio it gets divided into.

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the first step from the following.
1) Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

  1. $4$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The correct sequence is:

Step 1. Draw a line $L$ and consider a point $P$ outside the line.
Step 2. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step 3.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step 4. Draw line $PQ$
So the first step is $2$
Option $C$ is correct.

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

When a perpendicular is drawn to a given line and it also bisects it, then the perpendicular divides the line into

  1. $1:1$
  2. $1:2$
  3. $2:3$

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

Bisects means division into two equal parts .

When a perpendicular is drawn to a given line and it also bisects it, then the perpendicular divides the line into
Thus the correct answer is $1: 1$

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the third step from the following.
1) Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

  1. $4$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The correct sequence is:

Step 1. Draw a line $L$ and consider a point $P$ outside the line.
Step 2. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step 3.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step 4. Draw line $PQ$
So the third step is $4$
Option $A$ is correct.

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the second step from the following.
1)Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

  1. $4$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The correct sequence is:

Step 1. Draw a line $L$ and consider a point $P$ outside the line.
Step 2. Take $P$ as center and draw two arcs on line $L$ ans name the points $A$ and $B$ respectively.
Step 3.Taking $A$ and $B$ as centres one by one and keeping the same distance in compass , draw the arcs on other side of the plane .The point where these arcs intersect name that as $Q$
Step 4. Draw line $PQ$
So the second step is $3$
Option $B$ is correct.

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares
The steps for constructing a perpendicular from point $A$ to line $PQ$ is given in jumbled order as follows: $(A$ does not lie on $PQ)$
1. Join $R-S$ passing through $A$.
2. Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.
3. From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S$.
4. Draw a line $PQ$ and take a point $A$ anywhere outside the line.
The second step in the process is:
  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Correct sequence is :

Step 1 . Draw a line $PQ$ and take a point $A$ anywhere outside the line.

Step 2. Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.

Step 3. From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S.$

Step 4. Join $R−S$ passing through $A$.

So the second step is $2$.

Option $B$ is correct.