In this page we have *NCERT Solutions for Class 10 Maths Chapter 7:Coordinate Geometry* for
Exercise 7.1 . Hope you like them and do not forget to like , social_share
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(i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a,b), (-a,-b)

“Don’t you think ABCD is a square?” Chameli disagrees.

Using distance formula, find which of them is correct.

(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)

(ii) (-3, 5), (3, 1), (0, 3), (-1, -4)

iii) (4,5) ,(7,6), (4,3) (1,2)

(3, 6) and (– 3, 4).

Distance between the points AB is given by

Let P(0,0) and Q(36,15) be the given points.

Distance between the points PQ is given b

The position of town A and B can be represented as points P and Q respectively,So distance between town will be 39 km

Lets us denote point by P(1,5) , Q(2,3) and R(-2,-11)

If the points are not collinear, then we should be able to form the triangle

Lets us find the length of PQ, QR and PR by distance formula

Clearly None of these is true

PQ+QR=PR

PR+PQ=QR

PQ=QR+PR

Hence they are not collinear

Lets us denote point by P(5,-2) , Q(6,4) and R(7,-2)

Lets us find the length of PQ, QR and PR by distance formula

Now PQ =QR ,so it is an isosceles triangle

As per the figure given,The coordinates of the points A,B,C and D are (3,4), (6,7) ,(9,4) and (6,1)

Lets us find the length of AB, BC ,CD and AD by distance formula

So all the sides are equal. But we cannot still say that it is square as rhombus has all the sides equal also.

Now we know that a square has both the diagonal equal also,So lets us calculate the diagonal’s

Hence AC=BD

So it is a square.

So champa is correct

In these type of problem, we need to find of length of each segment, then check with the properties of different type of quadrilateral

i.e for points A,B,C and D

Line segments are AB,BC,AC,CD,AD and BD

We need to find the length of each of these

i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)

Here the side AB,BC,CD and AD are equal and diagonal AC and BD are equal. So this is a square

ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)

Now here AC+BC=AB

So that means ABC are collinear points.

So it is not a quadrilateral infact

iii) (4,5) ,(7,6), (4,3) (1,2)

Now AB=CD and BC=DA

Now it could be rectangle or parallelogram

But diagonal AC is not equal diagonal BD

So It is a parallelogram

Since the point lies on X axis, the point should be of the form (a,0)

Now (a,0) is equidistant from both the given points

Squaring both the sides

(x-2)

Solving it we get

x=-7

Acoording to the question

PQ=10

Squaring both the sides

y

(y+9)(y-3)=0

So y=-9 or 3

Now

QP=QR

Squaring both the sides

25+16=x

x= -4 or 4

So point R is either (4,6) or (-4,6)

Let the point P(x,y) is equidistant from the point Q( 3,6) and R(-3,4)

PQ=PR

Squaring both the sides

x

-12x-4y+20=0

Or

3x+y-5=0 ( dividing by -4)

Download Coordinate Geometry Exercise 7.1 as pdf

- Flash Back from Class IX notes
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- Distance formula
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- Section Formula
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- Area of triangle
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- How to Solve the line segment bisection ,trisection and four-section problem's
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- How to Prove three points are collinear
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- How to solve general Problems of Area in Coordinate geometry

- Coordinate Geometry Problem and Solutions
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- Coordinate Geometry Short questions
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- Coordinate Geometry 3 Marks Questions
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- Coordinate Geometry 5 Marks questions

Given below are the links of some of the reference books for class 10 math.

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.

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