Question

What is the distance between P(-3, -2) and Q(5, -2)?


12

14

10

8
2.
What is the distance between P(7, 0) and Q(8, 0)?


1

4

2

3
3.
What is the distance between points P(0, 4) and Q(3, 0)?


8

5

6

7
4.
What is the distance between points P(1, 7) and Q(9, -8)?


15

13

17

11
5.
Find the midpoint of segment P Q if P(4, 1) and Q(12, -5)?


(2, -8)

(8, -2)

(-8, -2)

(-2, 8)
6.
Find the midpoint of segment P Q if P(10, 2) and Q(8, 0)?


(9, 1)

(-9, -1)

(1, 9)

(-1, 9)
7.

Answer 1

Please teach me how to do this!

Answer 2

We can use the distance formula

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

Answer 3

So the equation will be (-3-2)^2 + ( -2+2)^2 ? @ohnweldon1993

Answer 4

For example with #1

"What is the distance between P(-3, -2) and Q(5, -2)?"

\(\large P(\color \red{-3}, \color \purple{-2}) Q(\color \green{5},\color \yellow{-2})\)
\[\large (\color \red{x_1}, \color \purple{y_1}) Q(\color \green{x_2},\color \yellow{y_2})\]

so we would have

\[\large \sqrt{(5 - (-3))^2 + (-2 - (-2))^2}\]

Answer 5

Does that make sense?

Answer 6

So in simplifying, we have

\[\large \sqrt{(5 + 3)^2 + (-2 + 2)^2}\]
\[\large \sqrt{(8)^2 + (0)^2}\]
\[\large \sqrt{64} = 8\]

Answer 7

And then for the midpoints on the last 2 questions we can basically do the same thing

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

Answer 8

yes, I understand the first one! thank you.
And the midpoint one... will you show me how to do it? @johnweldon1993

Answer 9

Of course :)

so lets use the last problem as the walkthrough

"Find the midpoint of segment P Q if P(10, 2) and Q(8, 0)?"

So we'll set it up again

\[\large P(\color \red{10}, \color \purple{2}) Q(\color \green{8},\color \yellow{0})\]

\[\large P(\color \red{x_1}, \color \purple{y_1}) Q(\color \green{x_1},\color \yellow{y_2})\]

so for the mid point we use the formula I wrote up there

\[\large Midpoint = (\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})\]
\[\large Midpoint = (\frac{10 + 8}{2} , \frac{2 + 0}{2})\]
\[\large Midpoint = (\frac{18}{2} , \frac{2}{2})\]
\[\large Midpoint = (9 , 1)\]

Answer 10

Sorry, up there is a little typo it should be

\[\large P(\color \red{x_1}, \color \purple{y_1}) Q(\color \green{x_2},\color \yellow{y_2})\]

*Just accidentally wrote \(\large x_1\) twice*

Answer 11

I got it :) Thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! @johnweldon1993

Answer 12

Anytime hun :)

Answer 13

did you receive a medal? @johnweldon1993

Answer 14

Oh, yes I did @chappy0729 thanks for that, dont do it for the medal but it was very nice of you ^_^

Answer 15

hahaha okay:) well thank you for helping me ! @johnweldon1993

Answer 16

Of course :) if you need anything else feel free to message me :)

Answer 17

Okay :) I will:p @johnweldon1993

Answer 18

:P