in an image the slanted rectangle starts at 0 over right 2 spaces. Then 2 more over to 4 up to 3 then left 2 and back to 0.what would it look after a rotation of 90 degrees about 0.
a)rectangle goes to the left in quadrant 2.
b)rectangle goes down in the 4 quadrant.
c)rectangle goes in 3 quadrant.
d)rectangle goes in 2 quadrant but faces a diffrent way.
I think it is B
(0,0) (2,0) (4,3) (2,3)
well, you could cut it out of cardboard :)
It goes to quadrant 2
The top face becomes the left face, so it faces a different way
so d
If you spin 90 deg left from quadrant 1, how could you be in quadrant 4 ?
The best way to solve these problems is to follow the instructions, draw the figure with the coordinates of each point, and then apply the transformation (rotation).
I will give you a kickstart by giving the coordinates of the figure (not a rectangle).
A(0,0)
B(2,0)
C(4,0)
D(4,3)
E(2,3)
A(0,0)
A 90° rotation has the transformation
R(O,90°)=(x,y)->(-y,x)
which means that a point such as D(4,3) will be transformed to D'(-3,4), meaning the negative y-coordinate (3) of D' become the x-coordinate of D', and the x-coordinate of D (4) becomes the y-coordinate of D', resulting in D'(-3,4).
Work on all the points to find the coordinates of the image, A'B'C'D'E'A'.
The appropriate answer will be shown on a graph on paper.
To determine the location of the slanted rectangle after a 90-degree rotation about the origin (0,0), let's break down the given information into steps.
Step 1: Starting Position
The rectangle starts at (0,0) and moves right 2 spaces.
Step 2: Move 2 Spaces Over to the Right
The rectangle moves 2 spaces over to the right from its starting position at (0,0), which brings it to the point (2,0).
Step 3: Move 4 Spaces Up
Next, the rectangle moves 4 spaces up from the point (2,0). So, it will be located at (2,4).
Step 4: Move 3 Spaces to the Left
The rectangle then moves 3 spaces to the left from the point (2,4), resulting in the new position of (-1,4).
Step 5: Return to the Origin
Finally, the rectangle moves back to the origin (0,0) by moving 2 spaces to the left. Therefore, it ends up at (-2,4).
Now, let's determine the new position of the rectangle after a 90-degree rotation about the origin (0,0). In a 90-degree rotation, the x and y-coordinates of a point swap with each other while the sign of one of them changes.
For the point (-2,4), after a 90-degree rotation:
- The x-coordinate of (-2,4) becomes the new y-coordinate: new y-coordinate = -2.
- The y-coordinate of (-2,4) becomes the new x-coordinate, with the sign changed: new x-coordinate = -4.
The new position of the rectangle after the rotation is (-4,-2).
Now, let's determine which quadrant this new position falls into. The quadrants are as follows:
- Quadrant 1: Positive x, Positive y
- Quadrant 2: Negative x, Positive y
- Quadrant 3: Negative x, Negative y
- Quadrant 4: Positive x, Negative y
The new position (-4,-2) falls into Quadrant 2 since both x and y coordinates are negative. However, it may not be facing the same direction as it did in the original position.
Therefore, the correct option is:
d) The rectangle goes to the 2nd quadrant but faces a different way.