Check all that apply
she did not find the correct vertex; it should be at (8, 5).
she used the wrong area formula; it should be a=1/2 b * h.
she used the wrong length for the base; it should be 7, like the given base.
she used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3.
she should have found a segment for the top that was not parallel to the bottom.

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the given base

# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3

Step-by-step explanation:

* Lets explain how to solve the problem

- She has three vertices of the parallelogram

- The vertices are (12 , 2) , (5 , 2) , (1 , 5)

∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates

∴ The length of the base of the parallelogram is 12 - 5 = 7 units

- In parallelogram each two opposite sides are equal and parallel

∴ The opposite side to the base is 7

∴ The x coordinate of the missing point equal the x-coordinate of the

  point (1 , 5) + the length of the base

∴ The x coordinate of the missing vertex  = 1 + 7 = 8

∵ The y-coordinate of the missing vertex is the same with the

   y-coordinate of the point (1 , 5)

∴ The y-coordinate of the missing vertex is 5

∴ The missing vertex is (8 , 5)

- The area of the parallelogram is A = bh, where b is the base of it

  and h is the height of this base

- Remember the height must be perpendicular on the base

∵ The perpendicular distance between the two parallel bases is the

  difference between the y-coordinates of the two points each one

  belong to one of the two parallel bases

∴ The height of the parallelogram = 5 - 2 = 3 units

∴ Its area = 7 + 3 = 21 units ²

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the

   given base

# She used a side length of the parallelogram for the height instead

  of a line segment perpendicular to the base; the height should be 3

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

2

step-by-step explanation: