Question

Find k so that the point p (-4, 6), lies on the line segment joining a(k, 10), b(3, -8)

Answer 1

Answer:

Step-by-step explanation:here is your answer

Answer 2

Answer:

The value of k is -6.

Step-by-step explanation:

Since, the equation of a line segment joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is,

$y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Thus, the equation of the line segment joining a(k, 10) and (3, -8) is,

$y-10=\frac{-8-10}{3-k}(x-k)$

$y-10=-\frac{18}{3-k}(x-k)$

If p (-4, 6), lies on the line segment then p will satisfy the equation of the line segment,

$6-10 = \frac{-18}{3-k}(-4-k)$

$-4(3-k) = -18(-4-k)$

$-12 + 4k = 72+18k$

$-12 - 72 = 14k$

$-84 = 14k$

$\implies k = -6$

Thus, the value of k would be -6.