Respuesta :
The equation for the perpendicular bisector of line segment XY is 2x + y = 7, the correct option is A.
What is the standard equation of a line?
The standard equation of a line is given by
y = mx+c
Here m is the slope and c is the y intercept
The slope can be determined by
m = (y₂ -y₁)/(x₂ -x₁)
The line segment XY has the points X(5, 7) and Y(–3, 3).
The slope of the line is,
m = ( 3 - 7) /( -3 - 5)
m = -4 / -8
m = 1 /2
The product of the slope of a line and a line perpendicular to it is -1.
( 1/2) * m' = -1
m' = -2
As it is a bisector , the midpoint of X and Y will be the point on the line.
Midpoint of XY is ( ( 5 -3)/2 , (7+3)/2 )
Midpoint of XY is ( 1 , 5)
The equation of the perpendicular bisector of line segment XY is,
y = -2x +c
5 = -2 + c
c = 7
So, the equation is,
y = -2x +7
2x +y = 7
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