Find k, if B(k, -5), C (1, 2) and slope of the line is 7.
Find k, if B(k, -5), C (1, 2) and slope of the line is 7.
Answer:-
Slope of the line BC is 7.
Slope of BC =
\[\frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - \left( - 5 \right)}{1 - k} = 7\]
\[ \Rightarrow \frac{7}{1 - k} = 7\]
\[ \Rightarrow 1 - k = 1\]
\[ \Rightarrow k = 0\]
Explanation:-
Given that the slope of the line BC is 7, we can use the slope formula to find the value of k.
The slope formula is:
slope = (y2 – y1) / (x2 – x1)
Substituting the values of the given points B(-5,2) and C(k,9), we get:
slope of BC = (9 – 2) / (k – (-5)) = 7
Simplifying the above equation, we get:
7(k + 5) = 7(7)
7k + 35 = 49
7k = 49 – 35
7k = 14
k = 2
Therefore, the value of k is 2.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 122)