The coordinates of the vertices of triangle ABC are A(1,6), B(2,9), and C(7,10). Identify A'''B'''C''' after the following transformations; reflection y=x, reflection x-axis, and translation (x -7, y + 4) respectively.

A'''(-1,3), B'''(2,2) and C'''(3,-3)

Step-by-step explanation:

Hello There!

So the first thing we need to do is reflect the coordinates given over the y = x line which would be a straight line across the origin with a rate of change of 1

The rule for a reflection over the y = x line is  (x,y) > (y,x)

so pretty much we're just flipping the y and x values

(1,6) ---> (6,1)

(2,9) ---> (9,2)

(7,10) ---> (10,7)

so the new coordinates of A'B'C' are A'(6,1) , B'(9,2), and C'(10,7)

Now we want to reflect the points over the x axis

The rule for reflection over the x axis is (x,y) > (x,-y)

so the x value stays the same and the y values sign just get flipped so if the y value was originally negative then it will change to positive vise versa

(6,1) ---> (6,-1)

(9,2) ---> (9,-2)

(10,7) ---> (10,-7)

So the coordinates of A''B''C'' are  A''(6,-1) , B''(9,-2), and C''(10,-7)

Our final step is to translate 7 units to the left 4 units up

so the rule would be (x,y) > (x - 7, y + 4)

6-7=-1 | -1+4=3

(6,-1) ---> (-1,3)

9-7=2 | -2+4=2

(9,-2) ---> (2,2)

10-7=3 | -7+4=-3

(10,-7) ---> (3,-3)

so the after the three transformations the coordinates would be

A'''(-1,3), B'''(2,2) and C'''(3,-3)

i do not know this sorry : (

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !