Respuesta :
The slope of the line t perpendicular to line s is 5/2
Slope m of line t = 5/2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the slope of the line s = m₁
Let the slope of the line t = m₂
Now , for the perpendicular lines ,
The product of the slopes of the perpendicular lines = -1
So , the equation is m₁ x m₂ = -1
Now ,
Let the first point be = A ( x₁ , y₁ )
Let the second point be = B ( x₂ , y₂ )
The line s passes through the point A ( 8 , 2 ) and B ( 3 , 4 )
The equation of line is given by the formula
y - y₁ = m ( x - x₁ )
And the slope of the line is calculated by
Slope m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )
On substituting the values in the equation , we get
Slope m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m₁ = ( 4 - 2 ) / ( 3 - 8 )
Slope m₁ = 2 / ( -5 )
Slope m₁ = -2/5
Now , the slope of the line s is m₁ = -2/5
And , The product of the slopes of the perpendicular lines = -1
So , Product of slope of s and Product of slope of t = -1
Substituting the values in the equation , we get
m₁ x m₂ = -1
-2/5 x m₂ = -1
Multiply by 5 on both sides , we get
-2m₂ = -5
Divide by -2 on both sides , we get
m₂ = 5/2
Therefore , the value of m₂ is 5/2
Hence ,
The slope of the line t perpendicular to line s is 5/2
Slope m of line t = 5/2
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