Question

If the point A (2,3), B( 5,k) and c (6,7) are collinear then k___ full solution

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The value of k is 6.

Step-by-step explanation:

Given 3 points A(2,3), B(5,k) and C(6,7) which are collinear we have to find the value of k.

Points are collinear if the slopes of any two pairs are equal.

$\text{Slope of AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{k-3}{5-2}$

$\text{Slope of BC}=\frac{y_2-y_1}{x_2-x_1}=\frac{7-k}{6-5}$

As lines are collinear slopes are equal

⇒ $\frac{k-3}{5-2}=\frac{7-k}{6-5}$

⇒ $k-3=2(7-k)$

⇒ $4k=21+3$

⇒ $k=6$

The value of k is 6.