Δabc with vertices a(-3, 0), b(-2, 3), c(-1, 1) is rotated 180° clockwise about the origin. it is then reflected across the line y = -x. what are the coordinates of the vertices of the image?

The coordinates of the vertices of the image are:

A"(0,-3) , B"(3,-2) and C"(1,-1)

Step-by-step explanation:

We know that if any point is rotated by 180° clockwise then the rule that holds this transformation is:

(x,y) → (-x,-y)

and also the rule that holds for the reflection of a point about the line y= -x is:

(x,y) → (-y,-x)

Hence, now when ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin the transformed  vertices are given by:

A(-3,0) → A'(3,0)

B(-2,3) → B'(2,-3)

C(-1,1) → C'(1,-1)

Also now when it is reflected across the line y=-x the points of the resulting image is:

A'(3,0) → A"(0,-3)

B'(2,-3) → B"(3,-2)

C'(1,-1) → C"(1,-1)

Hence,

A(-3,0) → A"(0,-3)

B(-2,3) → B"(3,-2)

C(-1,1) → C''(1,-1)

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!