Question

Find the distance between​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

(1)A(2,-3) and B(-2,3)

(2) P(5,0) and Q (2,-3)

To find:-

Find the distance between the following points ?

Solution :-

1)

Given points are A(2,-3) and B(-2,3)

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

Let (x2, y2) = (-2,3) => x2 = -2 and y2 = 3

We know that

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

The distance between the given two points A and B

=> AB =√[(-2-2)²+(3-(-3))²]

=> AB =√[(-4)²+(3+3)²]

=>AB =√[(-4)²+6)²]

=>AB = √(16+36)

=> AB =√52

=> AB =√(4×13)

=> AB =2√13 units

2)

Given points are P(5,0) and Q(2,-3)

Let (x1, y1) = (5,0)=> x1 = 5 and y1 = 0

Let (x2, y2) = (2,-3) => x2 = 2 and y2 = -3

We know that

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

The distance between the given two points P and Q

=> PQ =√[(2-5)²+(-3-0)²]

=> PQ =√[(-3)²+(-3)²]

=>PQ = √(9+9)

=> PQ =√18

=> PQ =√(2×9)

=> PQ=3√2 units

Answer :-

1) The distance between the two points A and B = √52 units or 2√13 units

2)The distance between the two points P and Q =√18units or 3√2 units

Used formulae:-

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