Math help please TY :3 HWAJDSK 10 POINTS REWARDING !!
1 answer:
I will do Point A carefully, The others I will indicate. Start with the Given Point A. Then do the translations
A(-1,2) Original Point
Reflection: about x axis:x stays the same; y becomes -y:Result(-1,-2)
T<-3,4>: x goes three left, y goes 4 up (-1 - 3, -2 + 4): Result(-4,2)
R90 CCW: Point (x,y) becomes (-y , x ) So (-4,2) becomes(-2, - 4): Result (-2, - 4)
B(4,2) Original Point
- Reflection: (4, - 2)
- T< (-3,4): (4-3,-2 + 4): (1 , 2)
- R90 CCW: (-y,x) = (-2 , 1)
C(4, -5) Original Point
- Reflection (4,5)
- T<-3,4): (4 - 3, 5 + 4): (1,9)
- R90, CCW (-9 , 1)
D(-1 , -5) Original Point
- Reflection (-1,5)
- T(<-3,4): (-1 - 3, 5 + 4): (-4,9)
- R90, CCW ( - 9, - 4)
Note: CCW means Counter Clockwise
The graph on the left is the same one you have been given.
The graph on the right is the same figure after all the transformations
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Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
