Respuesta :
Answer:
First, you must find the midpoint of the segment, the formula for which is
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
. This gives
(
−
5
,
3
)
as the midpoint. This is the point at which the segment will be bisected.
Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula
y
2
−
y
1
x
2
−
x
1
, which gives us a slope of
5
.
Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of
5
is
−
1
5
.
We now know that the perpendicular travels through the point
(
−
5
,
3
)
and has a slope of
−
1
5
.
Solve for the unknown
b
in
y
=
m
x
+
b
.
3
=
−
1
5
(
−
5
)
+
b
⇒
3
=
1
+
b
⇒
2
=
b
Therefore, the equation of the perpendicular bisector is
y
=
−
1
5
x
+
2
.
Related questions
What is the midpoint of the line segment joining the points (7, 4) and (-8, 7)?
How would you set up the midpoint formula if only the midpoint and one
Step-by-step explanation:
Answer:
[tex](2.5, -1.3)[/tex]
Step-by-step explanation:
the midpoint of the line segment with endpoints (3.5,2.2) and (1.5,-4.8)
To find midpoint we use formula
[tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]
(3.5,2.2) is (x1,y1)
(1.5,-4.8) is (x2,y2)
Plug in all the values in the formula
[tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]
[tex](\frac{3.5+1.5}{2} ,\frac{2.2-4.8}{2})[/tex]
[tex](2.5, -1.3)[/tex] is the midpoint
