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)