Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Find All Points

Find all points on the y-axis that are 6 units from the point (4, -3).

Any hints?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Find All Points

Find all points on the y-axis that are 6 units from the point (4, -3).

Any hints?

do distanceformula like they showed in the book
'on the y axis' means x=0 so points have x=0
you have D^2 = (4 - 0)^2 + (-3 - y) = 6^2
solve for y

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find All Points

Find all points on the y-axis that are 6 units from the point (4, -3).

Any hints?

do distanceformula like they showed in the book
'on the y axis' means x=0 so points have x=0
you have D^2 = (4 - 0)^2 + (-3 - y) = 6^2
solve for y

(4 - 0)^2 + (-3 - y) = 6^2

(16) - 3 - y = 36

13 - y = 36

-y = 36 - 13

-y = 23

y = 23/-1

y = -23

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find All Points

(4 - 0)^2 + (-3 - y) = 6^2

I think you need

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Find All Points

(4 - 0)^2 + (-3 - y) = 6^2

I think you need

Bob

i dropped the 'square' on the second parenthesis
thanks for catching that!

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find All Points

(4 - 0)^2 + (-3 - y) = 6^2

I think you need

Bob

Thank you, Bob. I will work it out again.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find All Points

(4 - 0)^2 + (-3 - y) = 6^2

I think you need

Bob

i dropped the 'square' on the second parenthesis
thanks for catching that!

(4 - 0)^2 + (y + 3)^2 = 6^2

(4)^2 + (y + 3)^2 = 36

16 + (y + 3)^2 = 36

(y + 3)^2 = 36 - 16

(y + 3)^2 = 20

sqrt{(y + 3)^2} = sqrt{20}

y + 3 = 2•sqrt{5}

y = 2•sqrt{5} - 3

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find All Points

That's good but

Find all points on the y-axis

If you do a sketch you'll see there will be two points. Get the other by using the minus square root.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find All Points

That's good but

Find all points on the y-axis

If you do a sketch you'll see there will be two points. Get the other by using the minus square root.

B

Ok.

Our two y-values are:

y = 2•sqrt{5} - 3

y = -2•sqrt{5} - 3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find All Points

That's it!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find All Points

That's it!

Bob

It certainly feels good to get the right answer. It creates a sense of personal accomplishment.