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2 answers:
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When a shape is rotated, it must be rotated around a point.
<em>To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by </em><em>.</em>
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From the question, we have:
--- the center of rotation
Let the vertices of the triangle be (x,y).
First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.
This gives:
Then the vertices are rotated by
<u />
<u>The rule of </u><u> rotation is:</u>
So, we have:
From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)
After rotation, the coordinates are calculated as follows:
Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)
Read more about rotations at:
Answer:
Option B.
Step-by-step explanation:
The given curve is
We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve .
Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .
Length of the rectangle = 2x
Width of the rectangle = y
Area of a rectangle is
Substitute the value of y from the given equation.
.... (1)
Differentiate with respect to x.
Equate , to find the critical points.
Divide both sides by 6.
The value of x can not be negative because side length can not be negative.
Substitute x=3 in equation (1).
The area of the largest rectangle is 108 square units.
Therefore, the correct option is B.