Question

Question #9cca2

Answer 1

`"The point that we are looking for is D(4,1)."`

Explanation:

`"1-draw the points A(1,2) and B(3,4)"`
`"2-draw a line segment AB"`
`"3-find midpoint of the line segment AB"`
`C(x,y)=((1+3)/2,(2+4)/2)" , "C(2,3)`

`"4-draw a line(black and dotted) passing C(2,3) and"`
`"perpendicular to the line segment AB"`

`"since the slope of the AB is 1,the slope of the black line is -1"`
`"we can find out the equation of black dotted line."`
`y-3=-1(x-2)`
`y=-1(x-2)+3`
`y=-x+2+3`
`y=-x+5`
`x+y=5`

`"now we have two equation."`

`2x-3y=5" "(1)`
`x+y=5" "(2)`

`"let us expand the equation (2) by 3"`

`3(x+y)=3*5`
`3x+3y=15" "(3)`

`"let us sum (1) and (3)"`

`2x-cancel(3y)+3x+cancel(3y)=5+15`

`5x=20`

`x=20/5=4`

`"now use (1) or (2)"`

`x+y=5`

`4+y=5`

`y=5-4`

`y=1`