Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

What is P_1?

The midpoint of the line segment from P_1 to P_2 is (5, -4).
If P_2 = (7, -2), what is P_1?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: What is P_1?

There's a quick way to get this using vectors.

The vector that takes you from P2 to M is (-2, -2)

So apply the same to M  to get P1

Bob

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: What is P_1?

There's a quick way to get this using vectors.

The vector that takes you from P2 to M is (-2, -2)

So apply the same to M  to get P1

Bob

I don't know much about vectors.

The midpoint of the line segment from P_1 to P_2 is (5, -4).
If P_2 = (7, -2), what is P_1?

Midpoint = [(x_1 + x_2)/2, (y_1 + y_2)/2]

Can you show using the Midpoint formula?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: What is P_1?

You don't have to know much. To 'travel' from P2 to M you need to go 2 left and 2 down. That's the vector.

So start at M and go another 2 left and 2 down.

The midpoint coords are [  (x1+x2)/2, (y1+y2)/2  ]

So you can make two equations, one for x and one for y. I'll give one here and leave the other as an exercise.

(x1 + 7)/2 = 5

Bob

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: What is P_1?

You don't have to know much. To 'travel' from P2 to M you need to go 2 left and 2 down. That's the vector.

So start at M and go another 2 left and 2 down.

The midpoint coords are [  (x1+x2)/2, (y1+y2)/2  ]

So you can make two equations, one for x and one for y. I'll give one here and leave the other as an exercise.

(x1 + 7)/2 = 5

Bob

Let me find x_1.

(x_1 + 7)/2 = 5

x_1 + 7 = 10

x_1 = 10 - 7

x_1 = 3

I now need to find find y_1.

I think the set up is this:

(3 + y_1)/2 = -4

3 + y_1 = -8

y/1 = -8 - 3

y_1 = -11

So, P_1 = (3, -11).

Yes?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: What is P_1?

(3 + y_1)/2 = -4

That should be (-2 + y_1)/2 = -4

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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: What is P_1?

(3 + y_1)/2 = -4

That should be (-2 + y_1)/2 = -4

Bob

Where did you get -2 inside the parentheses (-2 + y_1)?

Anyway:

(-2 + y_1)/2 = -4

-2 + y_1 = -8

y_1 = -8 + 2

y_1 = -6

P_1 = (3, -6)

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,208

Re: What is P_1?

Where did you get -2    P_2 = (7, -2)

(3, -6) is right

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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

Re: What is P_1?

Where did you get -2    P_2 = (7, -2)

(3, -6) is right

Bob

Wonderful. Thanks.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah