Question

if A(5,4),B(10,6)andC(-5,k) are three points on the same line what is the value of k?​

Answer 1

Answer:

it is answer of the question

Answer 2

Given

We have given three points A(5,4),B(10,6) and C(-5,k)

To Find

We have to find the value of k

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since ,the above all three points are on the same line then they are said to be collinear.

If all three points are collinear then their slopes must be equal.

e.g.,slope of AB=Slope of BC

$\sf \longmapsto\dfrac{6 - 4}{10 - 5} = \dfrac{k - 6}{ - 5 - 10}$

$\sf \longmapsto\dfrac{2}{5} = \dfrac{k - 6}{ - 15}$

Cross multiply to both sides

$\sf \longmapsto 2( - 15) = 5(k - 6)$

$\sf \longmapsto - 30 = 5k - 30$

$\sf \longmapsto - 30 + 30 = 5k$

$\sf \longmapsto5k = 0$

$\sf \longmapsto \bold{\red{k = 0}}$