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.
-3 -2 1
1 5 1
-6 -4 2
2 10 2
B. Draw the new image above in blue ink and label it XYZ.
Left corner of triangle labeled X is on (-6, 2) Top of triangle labeled Y is on (-4, 10) right corner of triangle labeled Z is on (2, 2)
C. Write a matrix to show a reduction of the polygon by ½.
(I'm confused on what to do here)
D. Draw the image above in red ink and label it ABC
A. dilation
The dilation matrix is correctly done, except the original matrix (for KLM) should be in alphabetical order of the vertices, which is
-2 1 -3
5 1 1
therefore you need to readjust the matrix of the dilated figure.
It is normal practice to create matrices in alphabetic order of the vertices. This way, the dilated matrix that reads X,Y and X will have correspondences K->X, L->Y, M->Z.
B. What you drew correctly represent the old dilated matrix. Now you need to repeat the task for the readjusted matrix.
C. "the polygon" appears to mean the original triangle KLM, even though it is not obvious.
D. I am sure you have no problem with this part.
To answer question C about the matrix to show a reduction of the polygon by ½, we can use the concept of scaling. When reducing the size of a shape, we divide the coordinates by the scale factor.
In this case, the scale factor is ½. So, we need to divide each coordinate of the original triangle by 2.
The original coordinates are:
L (1, 1)
M (-3, 1)
K (-2, 5)
To reduce by ½, we divide each coordinate by 2:
L (1/2, 1/2)
M (-3/2, 1/2)
K (-1, 5/2)
Now we can write the matrix representing this reduction:
1/2 -3/2 -1
1/2 1/2 5/2
Note that the original triangle and its reduction is a bit hard to visualize without actually drawing it. Let's move on to question D where we will draw the image in red ink and label it ABC.