Answer:
Option A. (4,4)
Step-by-step explanation:
step 1
Find the slope of the line k
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
[tex]m1*m2=-1[/tex]
The slope of the given line is [tex]m1=3[/tex]
so
The slope of the line k is
[tex]m2*(3)=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
step 2
Find the equation of the line k
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]point(1,5)[/tex]
substitute the values
[tex]y-5=-\frac{1}{3}(x-1)[/tex]
step 3
Verify if the line k pass through the given points
Remember that
If the line passes through a point, then the value of x and the value of y of the point must satisfy the equation of the line
Verify each case
case A) (4,4)
[tex]4-5=-\frac{1}{3}(4-1)[/tex]
[tex]-1=-\frac{1}{3}(3)[/tex]
[tex]-1=-1[/tex] ----> is true
therefore
The line k pass through the point (4,4)
case B) (-2,-5)
[tex]-5-5=-\frac{1}{3}(-2-1)[/tex]
[tex]-10=-1[/tex] -----> is not true
therefore
The line k not pass through the point (-2,-5)
case C) (3,6)
[tex]6-5=-\frac{1}{3}(3-1)[/tex]
[tex]1=-\frac{2}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (3,6)
case D) (9,-1)
[tex]-1-5=-\frac{1}{3}(9-1)[/tex]
[tex]-6=-\frac{8}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (9,-1)
