Question

If the points A(2, 3), B(5, k) and C(6, 7) are collinear, then the value of k is
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Answer 1

Answer:

k=6

Step-by-step explanation:

Since,the points are collinear

Slope of AB=Slope of BC

k-3/5-2=7-k/6-5

k-3/3=7-k/1

k-3=21-3k

4k=24

k=6

HOPE THIS HELPS............

Answer 2

Answer:

k = 6

Step-by-step explanation:

We are given that the points A(2, 3), B(5, k) and C(6, 7) are collinear

So, They lie in the same line

First find the equation line using two point slope form

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

$A=(x_1,y_1)=(2,3)\\B=(x_2,y_2)=(6,7)$

Substitute the values in the formula :

$y-3=\frac{7-3}{6-2}(x-2)$

$y-3=1(x-2)$

$y=x+1$

Since   A(2, 3), B(5, k) and C(6, 7) are collinear

So, Point B must satisfy the line equation

So, $y=x+1$

$k=5+1$

$k=6$

Hence the value of k is 6