Question

giving medals!

If the midpoint of two points is (5,-1) and one of the points is (4,-3), find the other point.

Answer 1

@aum

Answer 2

Well we know that the midpoint is found using

\[\large (\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})\]

Answer 3

We know the 'x' will come out to 5 and the y will come out to -1 so

\[\large \frac{x_2 + 4}{2} = 5\]
\[\large \frac{y_2 -3}{2} = -1\]

Answer 4

So you can solve for x2 and y2

Answer 5

whats x2 and y2

Answer 6

\(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 4}}\quad ,&{\color{blue}{ -3}})\quad &({\color{red}{ a}}\quad ,&{\color{blue}{ b}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ a}} + {\color{red}{ 4}}}{2}\quad ,\quad \cfrac{{\color{blue}{ b}} + {\color{blue}{ (-3)}}}{2} \right)=(5,-1)
\\ \quad \\
thus \qquad \cfrac{{\color{red}{ a}} + {\color{red}{ 4}}}{2}=5\qquad and\qquad \qquad \cfrac{{\color{blue}{ b}} + {\color{blue}{ (-3)}}}{2}=-1\)

Answer 7

That would be what you are solving for

x2 would be the x-coordinate of your point and y2 will be the y-coordinate of the point...

so for example for the 'x'...we need to solve

\[\large \frac{x_2 + 4}{2} = 5\] what does x2 equal?

Answer 8

6

Answer 9

Correct, that will be your 'x'....now what about 'y'?

Answer 10

1

Answer 11

(6,1)

Answer 12

Correct again!

So your point will be \(\large (6,1)\)

Answer 13

can you help me with one more

Answer 14

Find the distance between the following pairs of points: (-3, 6), (3, 2)

Answer 15

This we can just use the distance formula

\[\large d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 16

so whats x2 and x1 and y2 and y1=

Answer 17

Oh I see the confusion now...

You have 2 points...

Point 1 = (-3 , 6) (x1 , y1)
Point 2 = (3 , 2) (x2 , y2) the 1 and the 2 just represent which point the numbers are from

Answer 18

you mean 5,-1 and 4,-3????

Answer 19

"Find the distance between the following pairs of points: (-3, 6), (3, 2)"

Answer 20

ohh sorr confusing from the last problem lol

Answer 21

sorry

Answer 22

Lol no problem :)

Answer 23

so hold on would this be the answer

Answer 24

52?

Answer 25

Close but you're forgetting the square root again

\[\large d = \sqrt{(3 - (-3))^2 + (2 - 6)^2} = \sqrt{(6^2) + (-4)^2} = \sqrt{36 + 16} = \sqrt{52}\]

Answer 26

37?

Answer 27

....?

Answer 28

36+1

Answer 29

?

Answer 30

I'm confused on what you are getting? where are you getting the 36 and the 1?

Answer 31

you wrote it

Answer 32

@johnweldon1993

Answer 33

sq root of 36+1

Answer 34

\[\large d = \sqrt{(3 - (-3))^2 + (2 - 6)^2} = \sqrt{(6^2) + (-4)^2} = \sqrt{36 + 16} = \sqrt{52}\]

Answer 35

Oh wait, is it getting cut off for you?

\[\large d = \sqrt{(6^2) + (-4)^2} = \sqrt{36 + 16} = \sqrt{52}\]

Answer 36

7.21 but what the sq root form

Answer 37

2sq root 13?

Answer 38

The original distance formula is

\[\large d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 39

so im right

Answer 40

\(\large 2\sqrt{13}\) is indeed correct

Answer 41

ty!

Answer 42

Of course!