Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

---

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

---

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: What is P_1?

Where did you get -2    P_2 = (7, -2)

(3, -6) is right

Bob

Wonderful. Thanks.