Question

draw a copy of abcd on a grid. using another color, draw a copy of abcd on the grid in a different location with the same orientation, and label it qrst.
a. on another sheet of paper, write instructions that describe how to move abcd to the location of qrst.
b. exchange instructions with a partner. follow your partners instructions to draw a third shape efgh in another color on the same grid. compare your drawings. do your drawings look the same? explain.
c. communicate precisely what makes a set of instructions for this explore & reason a good set of instructions?

Explanation:

• Part A: To move \(ABCD\) to \(QRST\), we can use translation. Translation is a type of transformation that slides a figure without rotating or resizing it.
• Part B: If the instructions are precise (e.g., using coordinate - based movements like "move 5 units to the right and 3 units up"), the drawings of \(EFGH\) should look the same. If the instructions are ambiguous (e.g., "move a little to the right"), the drawings may differ.
• Part C: A good set of instructions should be specific. It should mention the type of transformation (translation, rotation, reflection). If it is a translation, it should state the number of units moved in the \(x\) - direction (horizontal) and \(y\) - direction (vertical). If it is a rotation, it should state the center of rotation, the angle of rotation, and the direction (clockwise or counter - clockwise). If it is a reflection, it should state the line of reflection.

Answer:

• Part A: Translate \(ABCD\) by moving each point of \(ABCD\) the same number of units in the same direction. For example, if we assume \(A(x_1,y_1)\) and \(Q(x_2,y_2)\), then move each point of \(ABCD\) by \((x_2 - x_1)\) units in the \(x\) - direction and \((y_2 - y_1)\) units in the \(y\) - direction.
• Part B: If the instructions are precise (e.g., using coordinate - based translation instructions), the drawings of \(EFGH\) will look the same. If the instructions are not precise (e.g., using vague terms like "a short distance"), the drawings may not look the same.
• Part C: A good set of instructions should clearly define the transformation (translation: number of units in \(x\) and \(y\); rotation: center, angle, direction; reflection: line of reflection) to ensure that the resulting figure is uniquely determined.