Question

see the picture please

Answer 1

This calculator is pretty handy at computing the distance between any two points

http://www.mathportal.org/calculators/analytic-geometry/distance-and-midpoint-calculator.php

Answer 2

let me know if it helps or not

Answer 3

i don't really get it.. do you know what the answer is?

Answer 4

are you able to type in the numbers in the boxes? The numbers correspond to the coordinates of the points

Answer 5

the calculator then shows step by step how to get the distance

Answer 6

no it doesn't let me type in numbers

Answer 7

try this then

http://www.mathwarehouse.com/calculators/distance-formula-calculator.php

Answer 8

the two points you'll enter are (-1,5) and (4,1)

Answer 9

this is what I get when I use the second link

http://prntscr.com/b2nf11

Answer 10

i got 6.4!

Answer 11

So the calculator is saying the exact distance (in terms of radicals) is \[\Large \sqrt{41}\]
which is approximately equal to `6.403124237`

round that to the nearest tenth

Answer 12

yep 6.4 is the answer

Answer 13

awesome! can you help me with some more please @jim_thompson5910 ? :)

Answer 14

sure

Answer 15

ok!

Answer 16

are you able to find the sides of that triangle?

Answer 17

no..

Answer 18

going from Joan to Gary, how many units do you count out? Count the number of spaces between the points

Answer 19

5?

Answer 20

yep, how about from Gary to Kash?

Answer 21

8

Answer 22

ok now we must use the distance formula to find the distance from Joan to Kash. Use that calculator and tell me what you get

Answer 23

whats are the two coordinates for both ?

Answer 24

I'll show you how to find Joan's coordinates. You tell me Kash's coordinates

Start at where the x and y axis cross. Notice you do NOT move left or right. You only move straight up. So because you don't move left or right, the x coordinate is 0. You move up 6 units so the y coordinate of Joan's location is 6

so the point where Joan is at is (0,6)

hopefully this makes sense? If so, then tell me Kash's location in terms of (x,y) point.

Answer 25

wait so whats the 5 and 8 for?

Answer 26

that will come later

Answer 27

5 and 8 are the side lengths of the triangle. We're trying to find the third side. We need the distance formula (which means we need the coordinates of the points)

Answer 28

The ultimate goal is to find the perimeter of this triangle

Answer 29

oh ok..

Answer 30

so do you see how I got (0,6) for Joan's location?

Answer 31

yea...

Answer 32

where is Kash located? what are his coordinates?

Answer 33

i got 5,1?

Answer 34

Start at where the x and y axis cross.

move to the right 5 units. The x coordinate is 5
move down 2 units. The y coordinate is -2

so Kash is located at (5,-2)

agreed?

Answer 35

agreed!

Answer 36

so to recap so far

Joan is at (0,6)
Kash is at (5,-2)

use the distance formula calculator and plug in those coordinates

Answer 37

i got 9.433981132056603

Answer 38

add that to the other sides

5+8+ 9.433981132056603 = 22.4339811320567

Answer 39

the perimeter is approximately 22.4339811320567 so she travels roughly 22 miles

I rounded to the nearest whole number

Answer 40

awesome!

What is the exact distance from (−5, 1) to (3, 0)?

square root of 63. units
square root of 65. units
square root of 67. units
square root of 69. units

Answer 41

use the calculator and it will step you through it to the answer

Answer 42

i got 65!

Answer 43

\(\Large \sqrt{65}\) I think you mean?

Answer 44

right i just didn't want to do that... lol :)

Answer 45

you can write `sqrt(65)` to mean \(\Large \sqrt{65}\)

Answer 46

but yes I got \(\Large \sqrt{65}\) as well

Answer 47

ok! next :)

Answer 48

@jim_thompson5910

Answer 49

go ahead

Answer 50

The leg of a right triangle is 5 units and the hypotenuse is 8 units. What is the length, in units, of the other leg of the triangle?

square root 39 units
39 units
square root 89 units
89 units

Answer 51

I'm assuming your teacher has taught you the Pythagorean Theorem? or no?

Answer 52

nope

Answer 53

so you've never heard of it til now?

Answer 54

well I've heard of it but i don't know what it is.. or how to use it

Answer 55

This page may be of help. If not, then let me know

https://www.mathsisfun.com/pythagoras.html

btw, `Pythagoras' Theorem` and `Pythagorean Theorem` are the same thing, just slightly different name

Answer 56

ok and no the website doesn't help

Answer 57

do you see how they put squares up to the sides of the triangle?

Answer 58

like here for example

https://www.mathsisfun.com/geometry/images/triangle-3-4-5-pyth.gif

Answer 59

the idea is that the blue square (16) adds to the yellow square (9) to get the red square (25)

9+16 = 25

Answer 60

why is this important? because it allows us to find the length of unknown sides in right triangles

Answer 61

ok so can we answer the question..

Answer 62

do you see how in the 3,4,5 triangle we have 3^2 + 4^2 equal to 5^2 ?

Answer 63

ok..

Answer 64

Is it possible that you're in the wrong lesson? A few lessons ahead maybe?

Answer 65

it seems strange your teacher wants you to do homework on topics the teacher hasn't covered yet

Answer 66

yea i know.. I'm homeschooled btw

Answer 67

@jim_thompson5910

Answer 68

`The leg of a right triangle is 5 units and the hypotenuse is 8 units`

Answer 69

Using the pythagorean theorem, we can say...


\[\Large a^2 + b^2 = c^2\]
\[\Large 5^2 + x^2 = 8^2\]
\[\Large 25 + x^2 = 64\]


solve for x and tell me what you get

Answer 70

i have to solve for x for each of them?

Answer 71

no those are my steps. They all link together (eg: notice how 5^2 turns into 25, 8^2 into 64)