Question

name: meridan callwell date class day 87a: determine the type of transformation nw determine the transformation that occurred in the graph below. explain how you know it is this transformation. explain how you know it is not the other 3 transformations. 1. the figure underwent a translation this is because... translation moves a figure without (details left unread) the preserved properties are... this is not a ____ because... this is not a __ because... this is not a ____ because...

Explanation:

• Translation: A translation slides a figure without rotating or resizing it. The shape and size of the figure remain the same, and the orientation (the way the figure "faces") is unchanged. In the graph, if we assume the black triangle is the original and the red one is the image, we can check if it's a translation by seeing if all points of the black triangle move the same distance in the same direction.
• Not a Rotation: A rotation turns a figure around a point. If it were a rotation, we would be able to identify a center of rotation and an angle of rotation. The orientation (the direction the figure "faces") would change. For example, a right - angled triangle rotated 90 degrees would have its legs pointing in different directions compared to the original. But in our case, the general "slant" and orientation (relative to the coordinate axes) of the triangle (if we assume a translation) doesn't suggest a rotational change around a point.
• Not a Reflection: A reflection flips a figure over a line (the line of reflection). If it were a reflection, we could find a line (like the x - axis, y - axis, or a diagonal line) such that each point of the original figure has a mirror - image point on the other side of the line. For example, reflecting a triangle over the y - axis would change the x - coordinates of its vertices (from positive to negative or vice - versa) in a symmetric way. But in a translation, there is no such line of symmetry that flips the figure.
• Not a Dilation: A dilation resizes a figure. If it were a dilation, the sides of the triangle would be proportionally longer or shorter. We can check the lengths of the sides of the black and red triangles (using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for the vertices). If it's a translation, the side lengths of the two triangles (original and image) are equal.

Answer:

• The transformation is a translation.
• Not a rotation: There is no center of rotation and the orientation (relative to the "direction" of the triangle's sides) is preserved (no turning around a point).
• Not a reflection: There is no line of reflection (no mirror - like flip over a vertical, horizontal, or diagonal line).
• Not a dilation: The side lengths of the two triangles (original and image) are equal (no resizing).