A triangle T has a vortices (3,-1),(5,-1) and (5,-4).draw and label the traingle T. M is the matrix (1 0)
( 0 -1). The triangle T is mapped on triangle T by the means of transformations M,draw and label T on your diagram. T has a vertices at (3,1),(5,1) and (5,4)
what's to do? Just draw the triangles. They even gave you the coordinates!
Just to make sure they weren't lying, do the math:
http://www.wolframalpha.com/input/?i=%7B%7B3,-1%7D,%7B5,-1%7D,%7B5,-4%7D%7D*%7B%7B1,0%7D,%7B0,-1%7D%7D
To draw and label triangle T, we need to plot the given vertices (3,-1), (5,-1), and (5,-4) on a coordinate plane.
1. Start by drawing the x-axis and y-axis intersecting at the origin (0,0).
2. Plot the first vertex at (3,-1). This point is 3 units to the right and 1 unit down from the origin.
3. Plot the second vertex at (5,-1). This point is 5 units to the right and 1 unit down from the origin.
4. Plot the third vertex at (5,-4). This point is 5 units to the right and 4 units down from the origin.
5. Connect the three plotted points with straight lines to form triangle T.
6. Label the vertices as A, B, and C accordingly.
To transform triangle T using the matrix transformation M, we need to multiply the matrix M by the coordinates of each vertex of triangle T.
1. Multiply each coordinate of vertex A (3,-1) by the matrix M:
New coordinate of A = (1 * 3) + (0 * -1) = 3 + 0 = 3 (x-coordinate)
(0 * 3) + (-1 * -1) = 0 + 1 = 1 (y-coordinate)
So, the new coordinate of vertex A after the transformation will be (3,1).
2. Multiply each coordinate of vertex B (5,-1) by the matrix M:
New coordinate of B = (1 * 5) + (0 * -1) = 5 + 0 = 5 (x-coordinate)
(0 * 5) + (-1 * -1) = 0 + 1 = 1 (y-coordinate)
So, the new coordinate of vertex B after the transformation will be (5,1).
3. Multiply each coordinate of vertex C (5,-4) by the matrix M:
New coordinate of C = (1 * 5) + (0 * -4) = 5 + 0 = 5 (x-coordinate)
(0 * 5) + (-1 * -4) = 0 + 4 = 4 (y-coordinate)
So, the new coordinate of vertex C after the transformation will be (5,4).
Now, plot the new coordinates (3,1), (5,1), and (5,4) on the same coordinate plane. Connect these points with straight lines to form the transformed triangle T' (the mapped triangle T).
Note: The labeling of the transformed triangle T' will remain the same as triangle T (A, B, C).