The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?
2 answers:
Answer:
C. (-2, -1)
Step-by-step explanation:
It can help to plot the points.
For rotation 180 degrees, the center of rotation is the midpoint of the segment joining the given point and its image. That means you want to find the other end of a segment with one end (-4, 1) and midpoint (-3, 0).
For center of rotation O, this means ...
O = (A +A')/2
2O -A = A'
A' = 2(-3, 0) -(-4, 1) = (-6+4, 0 -1) = (-2, -1)
The coordinates of the image are (-2, -1).
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Answer: The correct option is A, i.e., 7.5.
Explanation:
It is given that ABC is a triangle and BD is an altitude.
Since BD is an altitude, therefore the height of the triangle is BD and the base of the triangle is AC.
The distance formula to find the distance between two points is,
First, we find BD, where B(-1,4) and D(2,4).
So, the height of the triangle is 3.
Now, we find the value of AC, where A(2,1) and C(2,6).
So, the base of the triangle is 5.
The formula to find the area of a triangle is,
Therefore, the area of the triangle is 7.5 unit square and the correct option is A.
