Respuesta :
Answer:
k = 8
Step-by-step explanation:
For the points to be collinear, then the slopes of each pair of points must be equal.
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (2, 6)
m = [tex]\frac{6-2}{2+2}[/tex] = [tex]\frac{4}{4}[/tex] = 1
Repeat with
(x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (4, k)
m = [tex]\frac{k-6}{4-2}[/tex] = [tex]\frac{k-6}{2}[/tex], thus
[tex]\frac{k-6}{2}[/tex] = 1 ( multiply both sides by 2 )
k - 6 = 2 ( add 6 to both sides )
k = 8
You can use the fact that you can get equation of a line from two points and that collinear points are on same straight line.
The value of k for the given condition is 8
What is the equation of a line passing through two given points in 2 dimensional plane?
Suppose the given points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], the n the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
Using above method to find the value of k
The equation of the line passing through
[tex](x_1, y_1 ) = (-2,2)\\(x_2,y_2) = (2,6)[/tex]
is given by
[tex]y - 2 = \dfrac{4}{4}(x+2)\\\\y = x + 4[/tex]
Since given three points are collinear thus, the point (4,k) should satisfy the above equation as that equation is true for all its component point (and only for them).
Thus, putting y = k, x = 4, we get:
[tex]k = 4 + 4\\k = 8[/tex]
Thus,
The value of k for the given condition is 8
Learn more about collinear points here:
https://brainly.com/question/1593959
