Question

please help!!!
http://prnt.sc/cnqvqx

Reflection using ASA

Answer 1

use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You will use the slope formula for the sides that make up the given angle. If the slopes are the same, this proves the angles are congruent. You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles



part 2:

What line of reflection did you choose for your transformation?

How are you sure that each point was reflected across this line? Be sure to use complete sentences in your answer.

Answer 2

I already have:

wright bank (A) : (-3, -2)
cubic storage (C): (6, 3)
Geometric gem (B): (6, -3)

3 new points

wright bank' (A'): (2, -3)
cubic storage'(C'): (-6, -3)
geometric gem'(B'): (6, 3)

Answer 3

sorry its a little long, but I would appreciate some help!

Answer 4

what line of reflection did you use to get
the 3 new points ?

Answer 5

http://prnt.sc/cnsfio

Answer 6

OK,
Double check the original coords for the bank
the bank is two over (to the left) and 3 down
we write that as (-2,-3)
I think you did it backwards

Answer 7

sorry I always get those confused :/

Answer 8

does this look correct:
wright bank (A) : (-2, -3)
cubic storage (C): (6, 3)
Geometric gem (B): (6, -3)

sideways (x ) is always first
up/down (y) is always second

Answer 9

ah! yes that looks correct

Answer 10

now the reflection
you picked the line of reflection to be x=0 ( a vertical up/down line)

Answer 11

to "reflect" about the x=0 line, we keep the same y (2nd number), but multiply the x value by -1

can you follow that rule for
wright bank (A) : (-2, -3)
cubic storage (C): (6, 3)
Geometric gem (B): (6, -3)

what do you get ?

Answer 12

were the ones I had above right?

Answer 13

some look wrong, so it's better to just re-do it
the rule is not too hard: keep the 2nd number, but "negate" the x value

Answer 14

okay
for cubic storage would it be.. (-6, 3) ?

Answer 15

yes cubic storage would it be.. (-6, 3)

Answer 16

okay :) and geometric gem (-6, -3) ?

Answer 17

yes

Answer 18

wright bank (2, -3) ?

Answer 19

yes

now they want you to show that ABC and A' B'C' are congruent

Answer 20

we will be using formulas correct?

Answer 21

do i use the distance formula for AB and A'B'

and use the slope formula for AB and A'B' AND BC and B'C'

Answer 22

@phi

Answer 23

yes, distance formula and slope formula
for example
the distance from the bank to Geo is
(-2,-3) to (6,-3)
we can "count" and see the distance is 8

but using the formula
\[ d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2} \]
we get

\[ \sqrt{ (-2-6)^2 + (-3 - -3)^2 } \\
\sqrt{(-8)^2 + (-3+3)^2 }\\
\sqrt{ 64+0}\\
\sqrt{64}\\
8
\]

Answer 24

ah okay thank you and its the exact same thing for A'B' right?

Answer 25

except the x-values are different
but the calculation will still work out to 8

Answer 26

okay thank you! :)

Answer 27

@phi okay I just finished all of those but can you help with the last question on the reflection?

What line of reflection did you choose for your transformation? How are you sure that each point was reflected across this line? Be sure to use complete sentences in your answer.

Answer 28

the line is x=0

How are you sure that each point was reflected across this line?
The point and the reflected point are each the same "shortest distance" to the line of reflection (but on opposite sides)