Question

question 1-40
which transformation rule can be used to transform figure q to figure q?
grid with two figures q and q
options:

1. ((x, y) \to (-y, x))
2. ((x, y) \to (y, -x))
3. ((x, y) \to (-x, y))
4. ((x, y) \to (x, -y))

Explanation:

Step1: Analyze transformation rules

Recall the transformation rules for coordinate points:

• \((x,y)\to(-y,x)\): Rotation 90° counterclockwise.
• \((x,y)\to(y,-x)\): Rotation 90° clockwise.
• \((x,y)\to(-x,y)\): Reflection over y - axis.
• \((x,y)\to(x,-y)\): Reflection over x - axis.

Step2: Observe figure transformation

Figure Q (left) to figure Q' (right) seems to be a rotation. Let's take a vertex of figure Q. Suppose a vertex of Q is \((-4,-3)\) (approximate, from the grid). Let's test the rotation rules.

For rotation 90° counterclockwise: \((x,y)\to(-y,x)\). If we take a point from Q, say let's assume a point \((x,y)\) in Q. After applying \((x,y)\to(-y,x)\), the coordinates should match Q'.

Let's take a point from the left figure (Q). Let's assume a vertex of the left parallelogram: let's say \((-5,-3)\), \((-2,-3)\), \((-1,-4)\), \((-4,-4)\) (approximate). Now apply \((x,y)\to(-y,x)\) to \((-5,-3)\): we get \((3,-5)\)? No, wait, maybe better to look at the shape. The left figure is a parallelogram, the right is a rotated version. The transformation \((x,y)\to(-y,x)\) is rotation 90° counterclockwise, which matches the orientation change from Q to Q'.

Testing the other options:

• \((x,y)\to(y,-x)\): Rotation 90° clockwise, which would not match the orientation.
• \((x,y)\to(-x,y)\): Reflection over y - axis, the shape would be mirrored left - right, not rotated.
• \((x,y)\to(x,-y)\): Reflection over x - axis, shape would be mirrored up - down, not rotated.

So the correct transformation is \((x,y)\to(-y,x)\).

Answer:

\((x,y)\to(-y,x)\) (the first option, assuming the first option is \((x,y)\to(-y,x)\))