Find the distances between the following points.
(iii) R(-3a, a), S(a, -2a)

6. Find the distances between the following points.

(iii) R(-3a, a), S(a, -2a)

Answer:-

R(–3a, a), S(a, –2a)

[RS = sqrt{left( – 3a – a right)^2 + left( a – left( – 2a right) right)^2}]

[ = sqrt{16 a^2 + 9 a^2}]

[ = sqrt{25 a^2}]

[ = 5a]

Explanation:-

The given problem involves finding the distance between two points R and S in terms of the variable ‘a’.

Let’s first identify the coordinates of R and S. R is located at (-3a, a) and S is located at (a, -2a).

Using the distance formula, we can find the distance between R and S:

RS = sqrt[(a – (-3a))^2 + (-2a – a)^2]

= sqrt[(4a)^2 + (-3a)^2]

= sqrt[16a^2 + 9a^2]

= sqrt[25a^2]

= 5a

Therefore, the distance between R and S is 5a.

Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)