Question

Plot all points that are 3 units from the x-axis and 3 units from (5,4). How many did you find?

Answer 1

all points 3 units from the x axis are on y=3 and y=-3

the distance formula is
`D=√((x_1-x_2)^2+(y_1-y_2)^2)`
ok, one point is (5,4) and the other is (x,3) or (x,-3), find both

for (x,3) (the ones on y=3)


`3=√((5-x)^2+(4-3)^2)`

`3=√(x^2-10x+25+(1)^2)`

`3=√(x^2-10x+26)`
squaer both sides
9=x²-10x+26
minus 9
0=x²-10x+17
factor
we can't
using quadratic formula
x=5-2√2 or 5+2√2


for (x,-3)

`3=√((5-x)^2+(4-(-3))^2)`

`3=\sqrtx{x^2-10x+25+(7)^2}`

`3=\sqrtx{x^2-10x+25+49}`

`3=\sqrtx{x^2-10x+74}`
squaer both sides
9=x²-10x+74
0=x²-10x+65
solving using quadratic formula we get a false statment
no points



so the 2 points are

`(5+2√(2),3)` and
`(5-2√(2),3)`