###
**Co-ordinate Geometry Problems asked**

in SSC CGL exam are of various kinds. One such set of co-ordinate geometry

problems asked in the SSC CGL Exam needs you to find the distance between two

points. Read on for a clear understanding.

in SSC CGL exam are of various kinds. One such set of co-ordinate geometry

problems asked in the SSC CGL Exam needs you to find the distance between two

points. Read on for a clear understanding.

Co-ordinate

geometry formulas can be extremely helpful in solving co-ordinate geometry

problems asked in SSC CGL Exams. These co-ordinate geometry problems are simple

and you just need a basic understanding of the Cartesian system to be able to

solve them. In the second blog in our series of co-ordinate geometry, we will

discuss the various co-ordinate geometry formulas used to solve problems. So we

will start with discussing some co-ordinate geometry formulas and then move to

questions based on them. But before we move ahead you must quickly revise the

basics of co-ordinate geometry.

geometry formulas can be extremely helpful in solving co-ordinate geometry

problems asked in SSC CGL Exams. These co-ordinate geometry problems are simple

and you just need a basic understanding of the Cartesian system to be able to

solve them. In the second blog in our series of co-ordinate geometry, we will

discuss the various co-ordinate geometry formulas used to solve problems. So we

will start with discussing some co-ordinate geometry formulas and then move to

questions based on them. But before we move ahead you must quickly revise the

basics of co-ordinate geometry.

###
**Co-ordinate Geometry Formulas:**

Distance between 2 Points

Distance between 2 Points

The distance

between two points- A (x1, y1) and B (x2, y2)

in the plane xy is

between two points- A (x1, y1) and B (x2, y2)

in the plane xy is

The distance

of a point A (x1, y1) form the Origin, O (0, 0), in the

plane xy is

of a point A (x1, y1) form the Origin, O (0, 0), in the

plane xy is

The distance

between two points- A (x1, y) and B (x2, y) in the plane

xy is

between two points- A (x1, y) and B (x2, y) in the plane

xy is

The distance

between two points- A (x, y1) and B (x, y2) in the plane

xy is

between two points- A (x, y1) and B (x, y2) in the plane

xy is

###
**Set 1: Co- ordinate Geometry Problems**

based on Distance Formula

based on Distance Formula

A lot of

problems asked in SSC Exams can be solved by simply using appropriate co-ordinate

geometry formulas. These co-ordinate geometry formulas are simple to remember

and using smart calculation tricks will get us to the correct answer in just a

few seconds.

problems asked in SSC Exams can be solved by simply using appropriate co-ordinate

geometry formulas. These co-ordinate geometry formulas are simple to remember

and using smart calculation tricks will get us to the correct answer in just a

few seconds.

**Problem 1**

**:**If the distance

between two points is (0, -5) and (x, 0) is 13 units. What is the value of ‘x’?

**Solution 1:**

We know the

formula used to find distance between two points-

formula used to find distance between two points-

Now the

above formula can be used to find the value of x, substituting the given values

we get-

above formula can be used to find the value of x, substituting the given values

we get-

13 = √{ (x- 0)2 + (0- -5)2}

13 = √(x2 + 25)

By squaring

both sides-

both sides-

132

= x2 + 25

= x2 + 25

169- 25 = x2

144 = x2

x=

__+__12
Therefore the value of point x is

__+__12

**Problem 2**

**:**What is the distance

between the points (0, 0) and the intersecting point of the graphs x=2 and y=4?

**Solution 2:**

Just because

the question seems to be a little complicated on reading, does not imply that

it is actually complicated. Use of co-ordinate geometry formulas will help us

get the answer. So the formula to be used in this question from the above

co-ordinate geometry formulas is-

the question seems to be a little complicated on reading, does not imply that

it is actually complicated. Use of co-ordinate geometry formulas will help us

get the answer. So the formula to be used in this question from the above

co-ordinate geometry formulas is-

We know that

one of the points is the Origin. For the other point, let’s start by plotting a

graph. Now there are actually two points we are talking about here- (3, 0) and

(0, 4). Plot both these points on the xy plane and then extend the lines. Once

we do that, they intersect at a common point P, the co-ordinates for which will

be (3, 4).

one of the points is the Origin. For the other point, let’s start by plotting a

graph. Now there are actually two points we are talking about here- (3, 0) and

(0, 4). Plot both these points on the xy plane and then extend the lines. Once

we do that, they intersect at a common point P, the co-ordinates for which will

be (3, 4).

Now since

one of the points is the origin, we can use the formula-

one of the points is the origin, we can use the formula-

Distance= √(32 + 42)

Distance= √(9 +16)

Distance= √25

Distance= 5

So the distance between the origin and

point P is 5 units.

point P is 5 units.

This how

co-ordinate geometry problems can be solved- by using the appropriate formula,

from the list of co-ordinate geometry formulas.

co-ordinate geometry problems can be solved- by using the appropriate formula,

from the list of co-ordinate geometry formulas.

###
**Co-ordinate Geometry Formulas: Section**

Formulas

Formulas

If any point

P (x, y) divides the line segment joining the points A (x1, y1)

and B (x2, y2) in the ratio m: n internally then,

P (x, y) divides the line segment joining the points A (x1, y1)

and B (x2, y2) in the ratio m: n internally then,

If P is the

midpoint, in that case the ratio between m and n will be 1: 1 and the formula

will be-

midpoint, in that case the ratio between m and n will be 1: 1 and the formula

will be-

If any point

P (x, y) divides the line segment joining the points A (x1, y1)

and B (x2, y2) in the ratio m: n externally then,

P (x, y) divides the line segment joining the points A (x1, y1)

and B (x2, y2) in the ratio m: n externally then,

###
**Set 2: Co- ordinate Geometry Problems**

based on Section Formula

based on Section Formula

Co-ordinate

geometry problems asked in SSC Exams are also in section formulas. Though they

may appear complex and complicated, they can be solved easily by using co-ordinate

geometry formulas.

geometry problems asked in SSC Exams are also in section formulas. Though they

may appear complex and complicated, they can be solved easily by using co-ordinate

geometry formulas.

**Problem 1**

**:**Find the

point that divides the line segment joining the points (4, 5) and (-4, 1) in the

ratio 1:3 (i) internally (ii) externally.

**Solution 1:**

So we have

to find two sets of points- internal and external. The question is direct and

can be easily solved by using these two co-ordinate geometry formulas-

to find two sets of points- internal and external. The question is direct and

can be easily solved by using these two co-ordinate geometry formulas-

(i) Let us

start with the first part of the question, where the division is done internally.

Assume the point to be P (x, y)-

start with the first part of the question, where the division is done internally.

Assume the point to be P (x, y)-

PX=

[(1x-4) + (3×4)]/ (1+3) = (-4+12)/4 = 8/4 = 2

[(1x-4) + (3×4)]/ (1+3) = (-4+12)/4 = 8/4 = 2

Py=

[(1×1) + (3×5)]/ (1+3) = (1+15)/4 = 16/4 = 4

[(1×1) + (3×5)]/ (1+3) = (1+15)/4 = 16/4 = 4

P= (2, 4)

(ii) Moving

on to the second part of the question where the division is done externally.

Assume the point to be Q (x, y)-

on to the second part of the question where the division is done externally.

Assume the point to be Q (x, y)-

Qx=

[(1x-4) – (3×4)]/ (1-3) = (-4 -12)/ -2 = -16/ -2 = 8

[(1x-4) – (3×4)]/ (1-3) = (-4 -12)/ -2 = -16/ -2 = 8

Qy =

[(1×1) – (3×5)]/ (1-3) = (1-15)/-2 = -14/ -2 = 7

[(1×1) – (3×5)]/ (1-3) = (1-15)/-2 = -14/ -2 = 7

Q= (8, 7)

So the two

set of co-ordinates that we get are: (2,4) divides the line internally and

(8,7) divides the line externally.

set of co-ordinates that we get are: (2,4) divides the line internally and

(8,7) divides the line externally.

###
**Practice Problems based on Co- ordinate**

Geometry Formulas

Geometry Formulas

Question 1:

In the xy-coordinate system, the distance between (2 3,- 2) and (5 3, 3 2) and

is approximately-

a) 5.1 b) 7.7 c) 4.3 d) 3.8

Question 2: Consider

the three points in the x-y plane: P = (2, 4), Q= (7, 7), and R = (6, 0). Rank

these three points from closest to the origin, (0, 0), to furthest from the

origin

the three points in the x-y plane: P = (2, 4), Q= (7, 7), and R = (6, 0). Rank

these three points from closest to the origin, (0, 0), to furthest from the

origin

a) P, R, Q b) R, P, Q c) R, Q, P d) P,Q,R

Question 3:

Find the point that divides the line segment joining the points (4,5) and

(-4,1) in the ratio 1:3 (i) internally (ii) externally

Find the point that divides the line segment joining the points (4,5) and

(-4,1) in the ratio 1:3 (i) internally (ii) externally

a) (1, 2)

(4, 3) b) (2, 3) (5, 8) c) (2, 4) (8, 7) d) (3, 2) (6, 7)

(4, 3) b) (2, 3) (5, 8) c) (2, 4) (8, 7) d) (3, 2) (6, 7)

Question 4:

Find the co-ordinates of the point which divides the join of the points (2, 3)

and (5, -3) in the ratio 1:2 (i) internally (ii) externally

Find the co-ordinates of the point which divides the join of the points (2, 3)

and (5, -3) in the ratio 1:2 (i) internally (ii) externally

a) (3, 1)

(-1, 9) b) (4, 3)(7, 8) c) (1, 4) (2, 7) d)(3, 2) (6, 9)

(-1, 9) b) (4, 3)(7, 8) c) (1, 4) (2, 7) d)(3, 2) (6, 9)

Remember to

write the answer to the above questions in the comment section below.

write the answer to the above questions in the comment section below.

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