(i am new to this subject of algebra)
Use the figure to answer the following questions:
( a triangle with the bottom right corner of it labeled L with (1, 1) x y coordinates. Left corner of the triangle is labeled M at the (-3, 1) coordinates. the top of the triangle is labeled K at the (-2, 5) coordinates.
A. Write a matrix to show a dilation of the polygon by a factor of 2.
B. Draw the new image above in blue ink and label it XYZ.
C. Write a matrix to show a reduction of the polygon by ½.
D. Draw the image above in red ink and label it ABC
you'll have to do the drawings yourself. Not too hard, I expect.
For scaling the figure, just multiply all the coordinates by the scale factor (2 or 1/2) and plot the new points.
for scaling by 2, then
(1,1) -> (2,2)
(-3,1) -> (-6,2)
and so on.
No algebra involved at all, really.
A. To write a matrix that represents a dilation of a polygon, we need to multiply each of the coordinates by the dilation factor. In this case, the dilation factor is 2.
Let's go through each coordinate and perform the dilation:
Coordinate L: (1,1) x 2 = (2,2)
Coordinate M: (-3,1) x 2 = (-6,2)
Coordinate K: (-2,5) x 2 = (-4,10)
Now we can write the matrix for the dilation:
[2 0]
[0 2]
B. To draw the new image above in blue ink and label it XYZ, we need to find the new coordinates after the dilation.
The new coordinates are:
X: (2, 2)
Y: (-6, 2)
Z: (-4, 10)
Now you can use these coordinates to draw the triangle in blue ink and label it XYZ.
C. To write a matrix that represents a reduction of the polygon by 1/2, we need to divide each of the coordinates by the reduction factor. In this case, the reduction factor is 1/2.
Let's calculate the new coordinates after the reduction:
Coordinate L: (1,1) / 2 = (0.5,0.5)
Coordinate M: (-3,1) / 2 = (-1.5,0.5)
Coordinate K: (-2,5) / 2 = (-1,2.5)
Now we can write the matrix for the reduction:
[0.5 0]
[ 0.5 2.5]
D. To draw the image above in red ink and label it ABC, we need to find the new coordinates after the reduction.
The new coordinates are:
A: (0.5, 0.5)
B: (-1.5, 0.5)
C: (-1, 2.5)
Now you can use these coordinates to draw the triangle in red ink and label it ABC.