Question

geometry walkthrough for hardly human

Answer 1

the key to this problem is to find the distance from each vertex to the point (1,-2)

Answer 2

now, each of these distances get cut into 1/3 of the original length, and the new vertices are drawn

this can potentially become difficult to calculate but I do have some short-cuts you can use, based on the pythagorean theorem/triangle proportionality theorem

Answer 3

the bottom side is the easiest since it's exactly 9 units long and it's horizontal so we can simply draw the new line like so:

Answer 4

the line on the right hand side can be difficult to estimate but we can draw a right triangle instead like so:

Answer 5

this triangle is 3 units wide and 9 units tall, which are easy lengths to cut into (1/3) and draw a new line like so

Answer 6

we can use a similar principle for the middle line by drawing this triangle

Answer 7

after cutting these sides into (1/3) we get 2 and 3, and draw a new triangle like so:

Answer 8

then simply connect the new triangle like so:

Answer 9

and the new triangle in black is your dilated triangle

Answer 10

@hardlyhuman

Answer 11

Thank you so much, I really appreciate it.

Answer 12

Would you mind helping me with another, to make sure i got it right?

Answer 13

sure

Answer 14

Thank you

Answer 15

select one corresponding side from each of the two triangles (for example, the bottom leg)

Answer 16

the small triangle leg is (1/4) the length of the old triangle leg (2/8 = 1/4) so the dilation must have been 1/4

we add a negative sign to indicate the change in orientation (reflection across y = x)

so -1/4 = your answer

Answer 17

thank you so much! could I run a few more by you please?

Answer 18

sure

Answer 19

Thank you, btw I like your pfp

Answer 20

is this right?

Answer 21

I think the y-coordinate might be a bit off

Answer 22

Okay, could you help me with it please?

Answer 23

first we will calculate (3/5) of the distance between 5 and 19 which is (3/5)*14

then we add that to 5 to get the true coordinate

so 5 + (3/5)*14 so i get 67/5

Answer 24

Okay

Answer 25

Sorry so which one would be 67/5?

Answer 26

the y-coordinate

Answer 27

right

Answer 28

and thats the answer for it? sorry im running on 2 hours of sleep right now

Answer 29

your x-coordinate was correct

(16/5,67/5) = your answer

Answer 30

awesome, thank you

Answer 31

Is this one right?

Answer 32

for midpoints you will take the average of the x-coordinates, then the average of the y-coordinates

x coordinate = (9+2)/2
y-coordinate = (-8-5)/2

then ^ simplify those, using decimals if necessary

Answer 33

okay

Answer 34

would it be (11/2 , -13/2)

Answer 35

good, but they want decimals instead so

(5,5,-6.5) is it

Answer 36

*** 5.5

Answer 37

okay, thank you

Answer 38

is this right?

Answer 39

yup good

Answer 40

Is this one?

Answer 41

I'd say GH = MN is not actually true b/c the triangles are similar not necessarily congruent

everything else looks ok

Answer 42

thank you

Answer 43

yup good

Answer 44

yup good

Answer 45

i swear this is the last one

Answer 46

yup good

Answer 47

Thank you so much for all your help, I really appreciate it. Hope you have a good day :)

Answer 48

yeah, you too