Answer :
Answer:
The answer to your question is: k = 1
Step-by-step explanation:
Data
MN (0, -3) , (-2, -4)
AB (2, 5) , (4 , k)
Formula
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Process
Slope MN = [tex]\frac{-4 + 3}{-2 + 0}[/tex] = [tex]\frac{1}{2}[/tex]
Slope AB = [tex]\frac{k - 5}{4 - 2} = \frac{k - 5}{2}[/tex]
If the lines are perpendicular then,
[tex]- 2 = \frac{k - 5}{2}[/tex]
-4 = k - 5
k = -4 + 5
k = 1
The value of k is 1 which makes these segments perpendicular.
What is coordinate geometry?
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
The given coordinates are:-
MN (0, -3) , (-2, -4)
AB (2, 5) , (4 , k)
The formula for the slope is calculated as:-
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Calculate the slope MN and AB as below:-
Slope MN = ( -4 + 3 ) / ( -2 + 0) = 1 / 2
Slope AB = ( k - 5 ) / 2
If the lines are perpendicular then,
-2 = ( k - 5 ) / 2
-4 = k - 5
k = -4 + 5
k = 1
Therefore, the value of k is 1 which makes these segments perpendicular.
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