Answered

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Which point lies on the perpendicular bisector of the segment with endpoints M (7,5) and N (-1, 5)? step by step please

Sagot :

Which point lies on the perpendicular bisector of the segment with endpoints M (7,5) and N (-1, 5)?

step 1

Find the midpoint segment MN

so

the formula to calculate the midpoint between two points is equal to

[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the given values in the formula

[tex]\begin{gathered} (\frac{7-1}{2},\frac{5+5}{2}) \\ \\ (3,5) \end{gathered}[/tex]

step 2

Find the slope segment MN

m=(5-5)/(-1-7)

m=0/-8

m=0

that means

the segment MN is a horizontal line

the perpendicular line to a horizontal line is a vertical line

step 3

Find the equation of the perpendicular line

we know that

the line passes through the midpoint of segment MN

point (3,5)

therefore

the equation of the vertical line is

x=3

therefore

the answer is

all points with x-coordinate equal to 3 lies on the perpendicular bisector

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