MATH SOLVE

7 months ago

Q:
# The endpoints of a side of rectangle ABCD in the coordinate plane are at A (2, 11) and B (7, 1). Find the equation of the line that contains the given segment. The line segment is AD. The equation is y = .

Accepted Solution

A:

we know that

A (2, 11) and B (7, 1)

step 1

find the slope of a line AB

the slope m=(y2-y1)/(x2-x1)------> m=(1-11)/(7-2)---> m=-10/5----> m=-2

step 2

find the equation of a line AD

we know that

the segment AB and the segment AD are perpendicular

so

m1*m2=-1

m2=-1/m1-----> m2=1/2

with the slope m2=1/2 and the point A(2,11)

y-y1=m*(x-x1)------> y-11=(1/2)*(x-2)----> y=(1/2)x-1+11

y=(1/2)x+10----> y=0.5x+10

the answer is

the equation of a line AD is y=0.5x+10

see the attached figure

A (2, 11) and B (7, 1)

step 1

find the slope of a line AB

the slope m=(y2-y1)/(x2-x1)------> m=(1-11)/(7-2)---> m=-10/5----> m=-2

step 2

find the equation of a line AD

we know that

the segment AB and the segment AD are perpendicular

so

m1*m2=-1

m2=-1/m1-----> m2=1/2

with the slope m2=1/2 and the point A(2,11)

y-y1=m*(x-x1)------> y-11=(1/2)*(x-2)----> y=(1/2)x-1+11

y=(1/2)x+10----> y=0.5x+10

the answer is

the equation of a line AD is y=0.5x+10

see the attached figure