Find the ratio in which point T(-1, 6)divides the line segment joining the points P(-3, 10) and Q(6, -8).
Find the ratio in which point T(-1, 6)divides the line segment joining the points P(-3, 10) and Q(6, -8).
Let the ratio be k : 1.
Using section formula we have
\[- 1 = \frac{6k - 3 \times 1}{k + 1}\]
\[- 1 = \frac{6k - 3 \times 1}{k + 1}\]
\[ \Rightarrow - k - 1 = 6k - 3\]
\[ \Rightarrow - 1 + 3 = 6k + k\]
\[ \Rightarrow 2 = 7k\]
\[ \Rightarrow k = \frac{2}{7}\]
Thus, the required ratio is 2 : 7.
Explanation:-
The question prompt is missing, but based on the answer given, it appears to be asking for the ratio of the coordinates of a point using the section formula.
Assuming that is the case, we can use the given equation and solve for the ratio k:
Let the ratio be k:1. Using the section formula, we have:
-1 = (6k – 3)/ (k + 1)
Multiplying both sides by (k + 1), we get:
-1(k + 1) = 6k – 3
Expanding and simplifying:
- k – 1 = 6k – 3
5k = 2
k = 2/5
Therefore, the required ratio is 2:5.
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)