Calculate the coordinates of the newly translated points for each of the following:
A set of three points are given in the matrix \begin{bmatrix} -3 & -1 & -7\\-4 & -8 & -2 \end{bmatrix}. They are all translated using the transformation matrix \begin{bmatrix} 0 & 0 & 0 \\7& 7 & 7 \end{bmatrix}.
A set of three points are given in the matrix \begin{bmatrix} 2 & 7 & 5\\9 & 6 & 4 \end{bmatrix}. They are all translated using the transformation matrix \begin{bmatrix} 0 & 0 & 0 \\-6& -6 & -6 \end{bmatrix}.
Consider the following triangle:
Represent the points of the triangle in an array.
Translate each point of the triangle 7 units left and plot its graph on a coordinate plane.
Represent the points of the new triangle in an array.
Now, determine the transformation matrix.
Consider the following points:
A \left( - 2 , 1\right), B \left( - 7 , 1\right), C \left( - 7 , 3\right), D \left( - 2 , 3\right)Plot the points on a coordinate plane.
State the coordinates of the four points if each point is translated 10 units right.
Now, determine the transformation matrix.
Determine the transformation matrix for the following:
Two points will be translated 5 units left.
Three points will be translated 6 units down.
Three points will be translated 7 units up and 5 units right.
Consider the matrix of points \begin{bmatrix} 1 & 0 \\0 & 1 \end{bmatrix}.
Plot the points on a coordinate plane.
Reflect the pair of points over the y-axis and write the new points in a matrix array.
Given three points A \left(9, 4\right), B \left(0, 6\right), C \left(3, 4\right), reflect these over the y-axis and state the coordinates of the points of the new image.
Consider the following algorithm for multiplying two matrices:
\begin{bmatrix} a & b \\c & d \end{bmatrix} \times \begin{bmatrix} A & B & C \\X & Y & Z \end{bmatrix}=\begin{bmatrix} aA+bX & aB+bY & aC+bZ \\cA+dX & cB+dY & cC+dZ \end{bmatrix}
Use the algorithm for multiplying two matrices to calculate the following:\begin{bmatrix} -1 & 0 \\0 & 1 \end{bmatrix} \times \begin{bmatrix} 9 & 0 & 3 \\4 & 6 & 4 \end{bmatrix}
Now, write down the transformation matrix.
Consider the matrix of points \begin{bmatrix} 1 & 0 \\0 & 1 \end{bmatrix}.
Reflect this pair of points over the x-axis and write the new points in a matrix array.
Given three points A \left(10, 4\right), B \left(8, 3\right), C \left(4, 4\right), reflect these over the x-axis and state the coordinates of the points of the new image.
Calculate: \begin{bmatrix} 1 & 0 \\0 & -1 \end{bmatrix} \times \begin{bmatrix} 10 & 8 & 4 \\4 & 3 & 4 \end{bmatrix}
Now, write down the transformation matrix.
Consider the matrix of points \begin{bmatrix} 1 & 0 \\0 & 1 \end{bmatrix}.
Reflect this pair of points over the line y = x and write the new points in a matrix array.
Given three points A \left(10, 2\right), B \left(6, 6\right), C \left(6, 0\right), reflect these over the line y = x and state the coordinates of the points of the new image.
Calculate: \begin{bmatrix} 0 & 1 \\1 & 0 \end{bmatrix} \times \begin{bmatrix} 10 & 6 & 6 \\2 & 6 & 0 \end{bmatrix}
Now, write down the transformation matrix.
Consider the following points:
A \left(0, 0\right), B \left(5, 0\right),C \left(5, 3\right), D \left(0, 3\right)Plot the points on a coordinate plane.
Use the transformation matrix \begin{bmatrix} 3 & 0 \\0 & 1 \end{bmatrix} to transform the original points to its image.
Describe the transformation that has taken place.
Consider the following points:
A \left(0, 0\right), B \left(4, 0\right), C \left(4, 2\right), D \left(0, 2\right)Plot the points on a coordinate plane.
Use the transformation matrix \begin{bmatrix} 1 & 0 \\0 & 3\end{bmatrix} to transform the original points to its image.
Describe the transformation that has taken place.
Consider the following points:
A \left(0, 0\right),B \left(3, 0\right),C \left(3, 4\right), D \left(0, 4\right)Plot the points on a coordinate plane.
Use the transformation matrix \begin{bmatrix} 0.5 & 0 \\0 & 0.5\end{bmatrix} to transform the original points to its image.
Describe the transformation that has taken place.
Consider the points E \left(1, 0\right) and F \left(0, 1\right) in the given graph:
Rotate the points 90 \degree clockwise, and write the resulting points in a matrix.
Given the points A\left(1,-7\right), B\left(8,6\right), C\left(-2,-4\right), use the transformation matrix in part (a) to rotate the points of the image 90 \degree. Write the rotated points in a matrix.
Consider the points E \left(1, 0\right) and F \left(0, 1\right) in the given graph:
Rotate the points 180 \degree, and write the resulting points in a matrix.
Given the points A\left(0,-4\right), B\left(6,0\right), C\left(1,8\right), use the transformation matrix in part (a) to rotate the points of the image 180 \degree. Write the rotated points in a matrix.
Consider the points E \left(1, 0\right) and F \left(0, 1\right) in the given graph:
Rotate the points 90 \degree counterclockwise, and write the resulting points in a matrix.
Given the points A\left(6,-8\right), B\left(-7,7\right), C\left(-3,3\right), use the transformation matrix in part (a) to rotate the points of the image 90 \degree counterclockwise. Write the rotated points in a matrix.
Consider the two points with array\begin{bmatrix} 1 & 0 \\0 & 1\end{bmatrix}.
Determine the transformation matrix that reflects points over the x-axis.
Determine the transformation matrix that will rotate the points 90 \degree counterclockwise.
Consider the points A, B, C in the given graph.
Use the transformation matrix from part (a) to reflect the points A, B, C about the x-axis. Write the new points, A', B', C', in a matrix array.
Use the transformation matrix from part (b) to rotate the points A', B', C'. Write the new points in a matrix array.
Consider the two points with array\begin{bmatrix} 1 & 0 \\0 & 1\end{bmatrix}.
Determine the transformation matrix that reflects the points over the line y = x.
Determine the transformation matrix that will rotate points 90 \degree clockwise.
Consider the points A, B, C in the given graph:
Use the transformation matrix from part (a) to reflect the points A, B, C. Write the new points, A', B', C', in a matrix array.
Use the transformation matrix from part (b) to rotate the points A', B', C'. Write the new points in a matrix array.
Consider the two points with array: \begin{bmatrix} 1 & 0 \\0 & 1\end{bmatrix}.
Determine the transformation matrix that reflects points over the y-axis.
Determine the transformation matrix that will dilate points by scale factor 3 in all directions.
Consider the points A, B, C in the given graph:
Use the transformation matrix from part (a) to reflect the points A, B, C. Write the new points, A', B', C', in a matrix array.
Use the transformation matrix from part (b) to dilate the points A', B', C'. Write the new points in a matrix array.
Consider the two points with array\begin{bmatrix} 1 & 0 \\0 & 1\end{bmatrix}.
Determine the transformation matrix that rotates points 180 \degree.
Determine the transformation matrix that will reflect the points around the line y = - x.
Consider the points A, B, C in the given graph:
Use the transformation matrix from part (a) to rotate the points A, B, C. Write the new points, A', B', C', in a matrix array.
Use the transformation matrix from part (b) to reflect the points A', B', C'. Write the new points in a matrix array.