Answer:
* 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
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