Geometric of 1/3, 2/9, 4/27, 8/81, 16/243
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The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)
<h3>How to match the vertices of the polygon?</h3>The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.
The vertices of polygon ABCD are given as:
A = (4, 6)
B = (5, 3)
C = (4, 2)
D = (1, 2)
The rule of rotation about point C is:
(x,y) = (a + b - y, x + b - a)
Where:
(a, b) = (4, 2) --- the point of rotation.
So, we have:
(x,y) = (4 + 2 - y, x + 4 - 2)
(x,y) = (6 - y, x + 2)
The above means that:
A' = (6 - 6, 4 + 2) = (0,6)
B' = (6 - 3, 5 + 2) = (3,7)
C' = (6 - 2, 4 + 2) = (4,6)
D' = (6 - 2, 1 + 2) = (4,3)
Hence, the image of the rotation and their vertices (i.e. coordinates) are:
A' = (0,6)
B' = (3,7)
C' = (4,6)
D' = (4,3)
Read more about rotation at:
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Answer:
Step-by-step explanation:
We need to find the equation of the line perpendicular to the line 3x+2y=8 and passes through (-5,2).
The given line can be expressed as:
We can see the slope of this line is m1=-3/2.
The slopes of two perpendicular lines, say m1 and m2, meet the condition:
Solving for m2:
Now we know the slope of the new line, we use the slope-point form of the line:
Where m is the slope and (h,k) is the point. Using the provided point (-5,2):