Question

find the distance between the following points. (1) A (2,3) ; B (4,1). (2) P(-5,7) ;Q(-1,3). (3) (a,b) ; (-a,-b)​

Answer 1

Step-by-step explanation:

Given :-

1) A (2,3) ; B (4,1).

(2) P(-5,7) ;Q(-1,3).

(3) (a,b) ; (-a,-b)

To find :-

Find the distance between the following points?

Solution :-

I) Given points are A (2,3) ; B (4,1)

Let (x1, y1)=(2,3)=>x1=2 and y1 = 3

Let (x2, y2)=(4,1)=>x2=4 and y2=1

We know that

The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

On Substituting these values in the above formula then

=> Distance between A and B = AB

=> AB = √[(4-2)²+(1-3)²] units

=>AB = √[2²+(-2)²] units

=> AB= √(4+4) units

=> AB= √8 units

=> AB= √(2×2×2) units

=>AB= 2√2 units

The distance between A and B = √8 units

(or) 2√2 units

_______________________________

ii) Given points are P(-5,7) ;Q(-1,3).

Let (x1, y1)=(-5,7)=>x1= -5 and y1 = 7

Let (x2, y2)=(-1,3)=>x2= -1 and y2= 3

We know that

The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

On Substituting these values in the above formula then

=> Distance between P and Q = PQ

=> PQ = √[(-1-(-5))²+(3-7)²] units

=>PQ = √[(-1+5)²+(-4)²] units

=> PQ= √(4²+(-4)²) units

=> PQ= √(16+16) units

=>PQ= √32 units

=>PQ= 4√2 units

The distance between P and Q = √32 units

(or) 4√2 units

_______________________________

I) Given points are (a,b) ; (-a,-b)

Let (x1, y1)=(a,b)=>x1=a and y1 = b

Let (x2, y2)=(-a,-b)=>x2=-a and y2=-b

We know that

The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

On Substituting these values in the above formula then

=> Distance between (a,b) ; (-a,-b)

=> √[(-a-a)²+(-b-b)²] units

=> √[(-2a)²+(-2b)²] units

=> √(4a²+4b²) units

=> √[4(a²+b²)] units

=> 2√(a²+b²) units

The distance between given points = 2√(a²+b²)units

_______________________________

Answer:-

1. The distance between A and B = √8 units (or) 2√2 units
2. The distance between P and Q = √32 units (or) 4√2 units
3. The distance between given points = 2√(a²+b²)units

Used formulae:-

• The distance between two points (x1, y1) and (x2, y2) is
• √[(x2-x1)²+(y2-y1)²] units