Question

The distance between vertical lines k and m is 11 and the locations of points P and P' are given below.

P (-9,0) P' (9,0)

The distance between P and P' is given by PP' equals_______

Answer 1

Looks like they are trying to distract you with some of the information. Have you learned how to read coordinates? Basically, (x-coordinate, y-coordinate)?

Answer 2

yes

Answer 3

x-9, y 0

Answer 4

Correct, that's the location of P.

Answer 5

And for P' we have x is 9, y is 0

Answer 6

So, basically our first "house" P is located at -9, and our second "house" P' is located at 9. The y's are both the same, 0. With this information, do you have any ideas on how we might find the distance between the two "houses"?

Answer 7

-9-9

Answer 8

good, at that would be -18 right?

Answer 9

yes

Answer 10

Now, in math, we usually think of distance as always being positive. So the "distance" should be positive 18.

Answer 11

You can just take the absolute value of your answer.

Answer 12

The distance between P and P' is 18. Does that make sense? :)

Answer 13

yes

Answer 14

Great! You've got it then!

Answer 15

So does the 11 have nothing to do with it

Answer 16

That's correct! That might be important to figure out where P'' (double apostrophe) is, but if we are only looking for P and P', we have all the information we need with the coordinates.

Answer 17

if we needed to find PP" what would I do

Answer 18

Good question. Let's draw a picture so we can get a bird's eye view of what's happening.

Answer 19

Here is a "map" of everything we know about the question. Notice that P and P' are both 9 units away from line k. I've also marked the distance between line k and line m as 11.

Answer 20

Does that make sense so far?

Answer 21

yes

Answer 22

Perfect! From the picture you posted, we can assume that P and P' are the same distance from line k, and we can also assume that P' and P'' are the same distance from line m. These are "reflections".

Answer 23

ok

Answer 24

Now, we might not know much about P'', but we know a lot about P'. We can figure out how far P' is from line m.

Answer 25

Just by looking at the picture, you should be able to see that P' is 2 units from line m

Answer 26

ahhh yes

Answer 27

Aha! Right? 9 + 2 = 11. And now, for the good part. Since P'' is the same distance away, it is also 2 units away from line m.