Question

question 1 - 28
click to show whether each transformation on the coordinate plane preserves only angle or both distance and angle.
dilation of a quadrilateral by a scale factor of 2
translation of a rhombus 3 units to the right and then reflection across the x - axis
translation of a triangle 2 units to the left then dilation by a scale factor of 0.2 about the origin

Explanation:

Step1: Analyze dilation by scale factor 2

Dilation changes the distance (lengths of sides). For a quadrilateral dilated by a scale factor of 2, the angles remain the same (since dilation is a similarity transformation), but distances are multiplied by 2. So it preserves only angle.

Step2: Analyze translation and reflection

Translation (moving 3 units right) and reflection (across \(x -\)axis) are rigid transformations. Rigid transformations preserve both distance (lengths of sides) and angles. A rhombus after translation and reflection will have the same side - lengths and angles as the original.

Step3: Analyze translation and dilation

Translation (2 units left) is a rigid transformation (preserves distance and angle), but dilation by a scale factor of \(0.2\) (a similarity transformation) changes the distance (lengths of sides). The angles of the triangle remain the same (because similarity transformations preserve angles), but distances are scaled by \(0.2\). So it preserves only angle.

Answer:

Transformation	Preserves only angle	Preserves both distance and angle
Translation of a rhombus 3 units to the right and then reflection across the \(x -\)axis		\(\square\)
Translation of a triangle 2 units to the left then dilation by a scale factor of \(0.2\) about the origin	\(\square\)