Questions on Geometry: Length, distance, coordinates, metric length answered by real tutors!

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Question 166153: A line segment 5 units long has one of its ends at (3,1). The ordinate of the other end is 5. Find its abscissa.: A line segment 5 units long has one of its ends at (3,1). The ordinate of the other end is 5. Find its abscissa.
Answer by jojo14344(1023) About Me  (Show Source):
You can put this solution on YOUR website!

The line segment 5 units will serve as the distance between the points.
Just like Pyth.theorem, we use the formula,
distance^2=(x[2]-x[1])^2+(y[2]-y[1])^2
Given ---system(x[1]=3,x[2]=x[2],y[1]=1,y[2]=5)
Continuing,
5^2=(x[2]-3)^2+(5-1)^2
25=x[2]^2-6x+9+16
25=x[2]^2-6x+25 ---> cross(25)=x[2]^2-6x+cross(25)
x[2]^2-6x=0
x[2](x[2]-6)=0 -----> highlight(x[2]=6) ANSWER, abscissa
See graph,
drawing(300,300,-8,8,-8,8,graph(300,300,-8,8,-8,8),(green(line(3,1,6,1))),(blue(line(6,1,6,5))),(red(line(6,5,3,1)))) -- line segment 5 units (RED LINE) has points (3,1) & (6,5)
Thank you,
Jojo