How to find the unknown equation when given it is 5 units from x+1?

Question

Can someone please explain to me how to do question 21? Thank!

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Answer 1 · 2017-12-07T12:19:16

See below.

You are told #( h , k )# lies on the line #y=x+1#, if #h# and #k# are the #x# and #y# coordinates respectively then we can say for:

#y=x+1#

We have:

#k=h+1color(white)(88)#[ 1 ]

You are told the point is 5 units from point #( 0 , 2 )#, so using distance formula:

#5=sqrt((0-h)^2+(2-k)^2)#

#25=h^2+4-4k+k^2color(white)(88)#[ 2 ]

From equation [ 1 ]

#h=k-1#

Substitute into [ 2 ]

#25=(k-1)^2+4-4k+k^2#

#25=k^2-2k+1+4-4k+k^2#

#0=2k^2-6k-20#

Factor:

#(2k+4)(k-5)=0=>k=5 and k= -2#

Using these values of #k# in equation [ 1 ]:

#5=h+1=>h=4#

#-2=h+1=>h=-3#

So:

#( 4 , 5 )# and #( -3 , -2 )#

#h=4 , -3#

#k=5 , -2#

Graph:

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