Find the distances between the following points. (ii) P(-6, -3), Q(-1, 9)
6. Find the distances between the following points.
(ii) P(-6, -3), Q(-1, 9)
P(–6, –3), Q(–1, 9)
\[PQ = \sqrt{\left( - 6 - \left( - 1 \right) \right)^2 + \left( - 3 - 9 \right)^2}\]
\[PQ = \sqrt{\left( - 6 - \left( - 1 \right) \right)^2 + \left( - 3 - 9 \right)^2}\]
\[ = \sqrt{25 + 144}\]
\[ = \sqrt{169}\]
\[ = 13\]
Explanation:-
Given two points P(-6, -3) and Q(-1, 9), we can find the distance between them using the distance formula.
The distance formula is:
distance = sqrt((x2 – x1)^2 + (y2 – y1)^2)
Substituting the values of the given points, we get:
PQ = sqrt((-1 – (-6))^2 + (9 – (-3))^2)
PQ = sqrt((5)^2 + (12)^2)
PQ = sqrt(25 + 144)
PQ = sqrt(169)
PQ = 13
Therefore, the distance between the points P(-6, -3) and Q(-1, 9) is 13 units. Hope you like it
Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)