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Mathematics 79 Online
mikewwe13:

What are the coordinates of the point (−1, 6) after a reflection across the x-axis? A. (1, 6) B. (1, −6) C. (−1, −6) D. (−1, 6)

mikewwe13:

@Vocaloid

Vocaloid:

any ideas? simply multiply the y-coordinate by -1 and leave the x alone

mikewwe13:

-6

Vocaloid:

good so putting it together (-1,-6) = your solution

mikewwe13:

1 attachment
Vocaloid:

so any ideas? which out of the four choices might put the triangle in that new orientation?

mikewwe13:

Rotation of 90 and 180

Vocaloid:

hm not quite if you rotate it 90 clockwise you put the shape into QII and then the 180 would put it into QIV but the shape needs to be in QIII so clearly we only need one rotation the better choice is the 180 since it will change the shape from QI to QIII after that what do you think might be the next step?

mikewwe13:

REFLECT ACROSS THE X-AXIS AND ROTATION OF 180

Vocaloid:

be careful if you rotate across the x-axis you put it into QIV and then the 180 rotation will put it into QII after the 180 degree rotation we only need to translate 1 unit to the left so the two steps are 180 degree rotation + 1 unit to the left (be careful to put them in the right order)

mikewwe13:

180 degree rotation + 1 unit to the left are correct ?

Vocaloid:

yes

mikewwe13:

1 attachment
Vocaloid:

well let's check the points we already have (5,1) (8,1) and (8,6) (x,y) --> (y,x) means switch the x- and y-coordinates so your new points should be (1,5) (1,8) and (6,8) let me know if you want to try graphing and checking w/ me first

mikewwe13:

graph first

Vocaloid:

sure go ahead and try the new graph and i'll see if your points are good

mikewwe13:

|dw:1534798178144:dw|

Vocaloid:

awesome, the points are correct you can also tell by seeing how the two triangles are symmetric about the blue line

mikewwe13:

right but i don't know how can i do it on mine

mikewwe13:

how to write that on my pic of the problem ? cause i draw it the same as the other picture i posted

mikewwe13:

cause i always put the answer wrong

Vocaloid:

uh well idk how your program works but after you click polygon just click where the points (1,5) (1,8) and (6,8) are, make a triangle, and you should be good to go

mikewwe13:

LIKE THIS ?

1 attachment
Vocaloid:

hm the points are correct but find a way to connect the orange point and the (6,8) point into a triangle

mikewwe13:

ok i'll just leave it like that

mikewwe13:

1 attachment
Vocaloid:

have you tried clicking the orange dot and the (6,8) in succession?

Vocaloid:

anyway for this next one you need to write down the original points and apply the rule so the original points are (2,2) (4,-3) and (7,3) the rule is (x,y) --> (x+3,y-5) so simply add 3 to each xcoordinate and subtract 5 from each y-coordinate

mikewwe13:

,|dw:1534799345527:dw|

Vocaloid:

hm not quite let's take it one point at a time (2,2) using the rule from before, add 3 to x and subtract 5 from y to get (2+3,2-5) ---> (5,-3) so the new point should be at (5,-3) try to repeat this logic w/ the other points

mikewwe13:

like graph it ?

Vocaloid:

first do the calculations then graph apply the same logic to the point (4,-3) and see what the new point should be.

mikewwe13:

0.2

mikewwe13:

is the answer

mikewwe13:

then graph (4, -3)

Vocaloid:

may I ask how you got 0.2? remember, the rule is: 1. add 3 to the x-coordinate 2. subtract 5 from the y-coordinate apply these rules to the point (4,-3) .

Vocaloid:

let's review if you have a point (x,y) the first number (x) is called the x-coordinate and the second number (y) is called the y-coordinate so for (4,-3) the x-coordinate is 4 and the y-coordinate is -3 apply these two rules: 1. add 3 to the x-coordinate 2. subtract 5 from the y-coordinate lmk what you get

mikewwe13:

there i've just calculated them from adding to the left and subtracting to the right so those are the answers (5, 3) (7, 8) (10, 2)

Vocaloid:

check your calculations again remember, you must ~subtract~ 5 from the y-coordinate not add them so (2,2) becomes (5,-3) as we stated before. (4,-3) becomes (4+3, -3-5) = (7,-8) and (7,3) becomes (7+3,3-5) = (10,-2)

Vocaloid:

so now try plotting (5,-3) (7,-8) and (10,-2).

mikewwe13:

altogether or separate ?

Vocaloid:

you must plot them on the same graph you are given because that is what the question is asking

Vocaloid:

any progress? simply locate (5,-3) (7,-8) and (10,-2). on the graph and connect them into a triangle

mikewwe13:

1 attachment
mikewwe13:

Vocaloid ?

Vocaloid:

yeah i'm still here this one takes a bit of drawing out anyway, if you try sketching it out you will see that the new triangle first requires a 90 degree rotation counterclockwise so the rule for a 90 rotation counterclockwise is (-y,x) which means multiply the y-coordinate by -1 and then switch the coordinates try performing the calculations on the points and see what the next step might be from there

mikewwe13:

rotation of 90 and translations 2 units up

Vocaloid:

good, well done

mikewwe13:

What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin? A. (3, 2) B. (−3, 2) C. (−3, −2) D. (−2, 3)

Vocaloid:

well let's go off what we said before for a counterclockwise rotation, multiply the y-coordinate by -1 then switch the x and y coordinates what do you get?

mikewwe13:

-2

Vocaloid:

remember, a point has 2 coordinates so your answer must have 2 numbers not just 1 (2, −3) the y-coordinate is -3 so multiply -3 by -1 to get 3 then switch the coordinates

Vocaloid:

(2,-3) multiply the y-coordinate by -1 to get (2,3) then switch the coordinates to get (3,2) as your solution.

mikewwe13:

(-3,-2) whenever you move a point by 90° the coordinates flip and the sign depends on wherever the point lands.

mikewwe13:

that's i thought ?

Vocaloid:

(-3,-2) is a clockwise rotation not a counterclockwise rotation if you are in doubt try drawing the point out

Vocaloid:

|dw:1534803045718:dw|

Vocaloid:

so (3,2) is the only possible solution since it's the only choice w/ both coordinates positive.

mikewwe13:

are you good at history ?

Vocaloid:

not really sorry

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