Question

question 1
which transformation will preserve distance between points when applied to a figure in the (x, y)-coordinate plane?
(x,y)→(−x,y + 1)
(x,y)→(x + 2,−\frac{1}{2}y)
(x,y)→(3x,3y)
(x,y)→(2x,y)
c
b
d
a

Explanation:

Step1: Recall the properties of isometric transformations

Isometric transformations (like reflections, translations, rotations) preserve distances. A translation \((x,y)\to(-x,y + 1)\) is a combination of a reflection (over the \(y -\)axis, since \(x\to - x\)) and a translation (up by 1 unit, since \(y\to y + 1\)).

Step2: Analyze non - isometric transformations

For a transformation \((x,y)\to(x + 2,-\frac{1}{2}y)\), the \(y -\)coordinate is scaled by \(\frac{1}{2}\), which changes distances. For \((x,y)\to(3x,3y)\), it is a dilation with a scale factor of 3, which changes distances. For \((x,y)\to(2x,y)\), the \(x -\)coordinate is scaled by 2, which changes distances.

Answer:

A. \((x,y)\to(-x,y + 1)\)