Find the distance between the following pair of points:

(a) (−6, 7) and (−1, −5)

(b) (a+b, b+c) and (a−b, c−b)

(c) (asinα, −bcosα) and (−acos α, bsin α)

(d) (a, 0) and (0, b)

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Solution

The distance d between two points and is given by the formula

(i) The two given points are (−6, 7) and (−1, −5)

The distance between these two points is

Hence the distance is.

(ii) The two given points are

The distance between these two points is

Hence the distance is.

(iii) The two given points are and

The distance between these two points is

Hence the distance is.

(iv) The two given points are (a, 0) and (0, b)

The distance between these two points is

Hence the distance is.

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Similar questions

Find the distance between the following pair of points:

(i) (-6,7) and (-1,-5)

(ii) (a+b,b+c) and (a-b,c-b)

(iii) $(a s i n α, - b c o s α) a n d (- a c o s α, b s i n α)$

(iv) (a,0) and (0,b)

(a sin α, - b cos α)

(a cos α, - b sin α)

(2, 3), (4, 1)

(- 5, 7), (- 1, 3)

(a, b), (- a, - b)

Find the distance between the points :

(i) A(9, 3) and B (15, 11) (ii) A (7, -4) and B(-5, 1)

(iii) A(-6, -4) and B(9, -12) (iv) A (1, -3 ) and B (4, -6)

(v) P (a+b, a-b) and Q (a-b, a+b)

(vi) P (a sin α, a cos α) and Q (a cos α, - a sin α)

a sin α, - b cos α

- a cos α, b sin α

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