Answer:
(0,-4)
Step-by-step explanation:
we know that
Point C will be on a line perpendicular to segment AB that passes through the point B
step 1
Find the slope of AB
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
A(2,4),B(5,-1)
substitute
[tex]m=\frac{-1-4}{5-2}[/tex]
[tex]m_A_B=-\frac{5}{3}[/tex]
step 2
Find the slope of the line BC perpendicular to the segment AB
Remember that
If two lines are perpendicular, their slopes are opposite reciprocal ( the product of the slopes is -1)
[tex]m_A_B*m_B_C=-1[/tex]
we have
[tex]m_A_B=-\frac{5}{3}[/tex]
therefore
[tex]m_B_C=\frac{3}{5}[/tex]
step 3
Find the equation in point slope form of the line BC
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{5}[/tex]
[tex]B(5,-1)[/tex]
substitute
[tex]y+1=\frac{3}{5}(x-5)[/tex]
step 4
Verify each case
we know that
The point C must be satisfy the linear equation
Substitute the value of x and the value of y in the linear equation and compare the result
a) we have (0,-6)
substitute
[tex]-6+1=\frac{3}{5}(0-5)[/tex]
[tex]-5=-3[/tex] ----> is not true
therefore
The ordered pair is not a possible location of point C
b) we have (0,-4)
substitute
[tex]-4+1=\frac{3}{5}(0-5)[/tex]
[tex]-3=-3[/tex] ----> is true
therefore
The ordered pair is a possible location of point C
c) we have (8,6)
substitute
[tex]6+1=\frac{3}{5}(8-5)[/tex]
[tex]7=\frac{9}{5}[/tex] ----> is not true
therefore
The ordered pair is not a possible location of point C
d) we have (8,4)
substitute
[tex]4+1=\frac{3}{5}(8-5)[/tex]
[tex]5=\frac{9}{5}[/tex] ----> is not true
therefore
The ordered pair is not a possible location of point C
