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

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

1 Answer
Dec 7, 2017

See below.

Explanation:

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

y=x+1y=x+1

We have:

k=h+1color(white)(88)k=h+188[ 1 ]

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

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

25=h^2+4-4k+k^2color(white)(88)25=h2+44k+k288[ 2 ]

From equation [ 1 ]

h=k-1h=k1

Substitute into [ 2 ]

25=(k-1)^2+4-4k+k^225=(k1)2+44k+k2

25=k^2-2k+1+4-4k+k^225=k22k+1+44k+k2

0=2k^2-6k-200=2k26k20

Factor:

(2k+4)(k-5)=0=>k=5 and k= -2(2k+4)(k5)=0k=5andk=2

Using these values of kk in equation [ 1 ]:

5=h+1=>h=45=h+1h=4

-2=h+1=>h=-32=h+1h=3

So:

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

h=4 , -3h=4,3

k=5 , -2k=5,2

Graph:

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