Question

Okay, so I have a few problems to do, but I have no clue how to solve them. It is geometry proofs using the distance formula I will post the pictures here

Answer 1

there are the first 3 problems. If anyone is patient enough to stay and help me with them until I get it would be greatly appreciated

Answer 2

do you know the formula to find slope given 2 points?

Answer 3

y2-y1
------= slope?
x2-x1

Answer 4

looks right. how would you go about finding the slope of AC?

Answer 5

A(0,0) C(a,a)
a-0
----= ?
a-0

Answer 6

1

Answer 7

you can simplify it because a-0=a and a/a=1

Answer 8

okay, I get it that part.

Answer 9

try bd

Answer 10

B(a,0) D(0,a)

a-0 a
---- = --= -1?
0-a -a

Answer 11

correct. what do you know about the slopes of perpendicular lines?

Answer 12

You have to take the reciprocal of the original slope. Like 1/3 would be -3/1 or just -3

Answer 13

exactly. so we have slopes 1 and -1 of AC/BD respectively

Answer 14

what do es that mean

Answer 15

Line AC is perpendicular to line ___
would it be BD

Answer 16

yep

Answer 17

wow, okay that was easy. Now it's the other ones that scare me haha

Answer 18

the 2nd one looks bleh :/
let's start with P

use the fact that the midpoint for \((x_1,y_1) \text {and}(x_2,y_2)\) is \((\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\)

Answer 19

okay, I know how to solve for midpoint but p has a two in it and I'm not sure where that is coming from

Answer 20

what do you mean?

Answer 21

P= 0+2a\2 Where is the 2a part from on the diagram?

Answer 22

P is the midpoint of A and B, right? so our x coordinate is half (you can think of it as the average) of the sum of the 2 x coordinates

0+2a

Answer 23

the 0 is the x coord of A
the 2a is the x coord of B

Answer 24

ooohhh, okay! so they're meeting in the middle of P I was thinking it was using the points of P. Makes so much more sense now.

Answer 25

do you want to fill in the rest of the stuff for P?

Answer 26

or does anything else need explaining

Answer 27

I need to kind of be walked through it. This thing online is so confusing so when someone is explaining it me it makes more sense.

Answer 28

i'll try writing it out then show it to you

Answer 29

cool, cool
that works