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)